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, Foreword
To those who are currently following the Finance for Pre-Master course at Tilburg University, here are
some tips and tricks in order to pass your final exam. The weight of the final exam is primarily on
financial options (chapter 20 and 21). To illustrate, in the 2019/2020 final exam, 45% of all points that
could be scored came from questions about options (9 MC questions and 2 open questions). The mean
grade for the final exam was a 4.3 according to Canvas, but it most likely was a lot higher, since a lot of
people passed this exam. Ultimately, only 53% of all 186 participants passed the entire course on the
first try according to Osiris.
Each chapter in this summary has been carefully constructed using the information that was provided
during the lectures from professor Crego and Verboven, as well as by their PowerPoint slides. Moreover,
I have taken the effort to copy the questions from each quiz as well as the answers and have expanded
the answers when necessary. Furthermore, I have used the questions from the mock exam, final exam
and resit from 2019/2020 and grouped them per chapter. This ensures that you can practice enough and
get a good grade. At the end of the document you can find the most important formulas for each chapter.
Use this document at your own discretion. I am by no means a finance expert and this document is bound
to contain some minor mistakes. If you spot any mistakes or errors, or if you have any questions you
can always send me a message on LinkedIn.
Good luck!
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, Table of contents
Foreword ................................................................................................................................................. 2
Chapter 20: Financial options.................................................................................................................. 5
20.1 Option basics ............................................................................................................................... 5
20.2 Option payoffs at expiration ........................................................................................................ 5
20.3 Option payoff plots ...................................................................................................................... 6
20.4 Combinations of options ............................................................................................................. 9
20.5 Put-call parity – European options ............................................................................................ 11
20.6 Exercising options early ............................................................................................................ 11
20.7 Factors impacting option prices................................................................................................. 12
Quiz Chapter 20..................................................................................................................................... 13
Exam questions chapter 20 .................................................................................................................... 18
Chapter 21: Valuing options.................................................................................................................. 23
21.1 The binomial option pricing model ........................................................................................... 23
21.2 Multinomial option pricing model............................................................................................. 25
21.3 Black-Scholes option pricing model ......................................................................................... 27
21.4 Risk-neutral probabilities .......................................................................................................... 29
21.5 Risk and return of an option ...................................................................................................... 29
21.6 Options and corporate finance ................................................................................................... 30
Quiz Chapter 21..................................................................................................................................... 32
Exam questions chapter 21 .................................................................................................................... 37
Chapter 23: Raising equity capital ........................................................................................................ 41
23.1 Equity financing for private companies .................................................................................... 41
23.2 The initial public offering (IPO)................................................................................................ 42
23.3 IPO puzzles................................................................................................................................ 43
23.4 The seasoned equity offering (SEO) ......................................................................................... 43
Quiz Chapter 23..................................................................................................................................... 44
Exam questions chapter 23 .................................................................................................................... 49
Chapter 24: Debt financing ................................................................................................................... 50
24.1 Types of debt ............................................................................................................................. 50
24.2 Bonds ......................................................................................................................................... 50
24.3 Debt covenants .......................................................................................................................... 51
24.4 Repayment provision ................................................................................................................. 51
Quiz chapter 24 ..................................................................................................................................... 52
Exam questions chapter 24 .................................................................................................................... 56
Chapter 25: Leasing............................................................................................................................... 58
25.1 Basics of leasing ........................................................................................................................ 58
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, 25.2 Accounting, tax and legal consequences of leasing .................................................................. 58
25.3 The leasing decision .................................................................................................................. 59
25.4 Reasons for leasing .................................................................................................................... 60
Quiz chapter 25 ..................................................................................................................................... 61
Exam questions chapter 25 .................................................................................................................... 64
Chapter 28: Mergers and acquisitions ................................................................................................... 66
28.1 Background info ........................................................................................................................ 66
28.2 Reasons to acquire ..................................................................................................................... 66
28.3 The takeover process ................................................................................................................. 67
28.4 Takeover defences ..................................................................................................................... 67
28.5 Leveraged buyouts (LBOs) ....................................................................................................... 68
Quiz chapter 28 ..................................................................................................................................... 70
Exam questions chapter 28 .................................................................................................................... 74
Chapter 30: Risk management .............................................................................................................. 78
30.1 Insurance ................................................................................................................................... 78
30.2 Insurance pricing ....................................................................................................................... 78
30.3 Hedging with forward and future contracts ............................................................................... 79
30.4 Interest rate risk ......................................................................................................................... 79
Quiz chapter 30 ..................................................................................................................................... 81
Exam questions chapter 30 .................................................................................................................... 85
Formulas ................................................................................................................................................ 88
Black-Scholes formula & Gaussian cumulative distribution table ........................................................ 90
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, Chapter 20: Financial options
20.1 Option basics
The definition of a financial option is: a contract that gives it owner the right (not the obligation) to
purchase or sell an asset at a fixed price at some date. A call option gives its owner the right to buy an
asset. A put option gives its owner the right to sell an asset. Exercising an option means that the holder
of the option enforces the agreement and buys/sells the asset at the agreed-upon price. The
strike/exercise price is the price at which the option holder buys/sells the asset when the option is
exercised. The expiration date is the last date on which the option holder has the right to exercise the
option. The option buyer/holder is the one that holds the right to exercise the option and has a long
position in the contract and pays a premium. The seller/writer sells the contract and has a short
position in the contract and earns a premium.
The terminology above is crucial to understanding options, so learn these first before continuing, as
things will get more complicated! Some of these terms are replaced by single letters later on. The
exercise/strike price is usually referred to as ‘K’, the price of the underlying asset is usually ‘S’ and
the expiration date is ‘T’. A call is referred to as ‘C’ and a put as ‘P’. These will be used extensively
in the next chapters!
There are different kinds of options, the two primary ones are American and European options. Both
have nothing to do with the location where the options are traded, they just happen to have these names.
American options allow their holders to exercise the option at ANY time up to and including the
expiration date. European options can only be exercised on the expiration date. Furthermore, stock
options are traded on organized exchanges and all traded options expire on the Saturday following the
third Friday of the month. The prices of 1 single option is quoted on these exchanges, but buying/selling
is done in contracts of 100.
An option that is at-the-money is an option of which the exercise price is usually equal to the price of
the underlying asset/stock price (S=K). An in-the-money option is an option whose value, if exercised,
is immediately positive: for a call S>K, for a put S<K. An out-of-the-money option is an option whose
value would be very negative if immediately exercised: for a call S<K, for a put S>K.
Why would you trade options? The primary reason for firms to consider buying/selling options is risk
management/hedging. Picture a firm that extracts oil and has extraction costs of €60 per gallon.
Today’s oil price is €70 per gallon. A huge drop in oil prices could reduce its profit margin from €10 to
€0. It therefore hedges using a put option. It buys a put option (so it is long) and when the price drops it
makes a profit. If the price actually increases it doesn’t earn anything, but it only has to pay the premium
(which is €0.7). Its profit margin is now fixed at €9.3 and protected from a drop in oil prices, where its
profit margin increases as long the price drops until the contract expires. Speculation is another reason.
Options offer high leverage which means that an investor which only has €1000 to invest, could use
leverage to increase its total amount of invested wealth. If it leverages up by x100 its investable wealth
increases to €100,000 and a 1% profit now equals a 100% profit (€1000). Similarly, a 1% loss means
that the investor loses 100%. Furthermore, options can be combined (we will see this in the next chapter)
which allow investors to not only bet on stock prices going up or down, but also on the volatility of
assets.
20.2 Option payoffs at expiration
Call options (long)
The value of a long position in a call at expiration is as follows: if S (the price of underlying) is > K
(strike price), we buy at K, and sell at S. Our payoff is S – K. If S is below K (S < K) we don’t exercise
the option and simply earn 0 (remember that we have already paid a premium, so we actually lose
money, but the payoff simply refers to the difference in S and K!).
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,To illustrate, if the price (S) of one AAPL stock is 310 and our exercise price (K) is 300, the payoff of
our call is S – K ➔ 310 – 300 = 10. If the price of 1 AAPL stock is 290, it is below the exercise price
and our payoff is 290 – 300 = 0 (remember, we don’t exercise and simply let the contract expire at the
strike price of 300!).
The value of a long call option (C) can thus be generalized as C = max(S – K, 0). ‘max(S – K, 0)’
mathematically expresses that the value is either the positive value of the difference between S – K or 0
if the difference is negative.
Put options (long)
The value of a long position in a put option is the exact opposite. If S is below K (S < K) we exercise
the option. We sell at K, buy at S and we ultimately get K – S. If S is above K (S > K) we don’t exercise
the put option and simply get 0.
To illustrate, if the price (S) of one AAPL stock is 310 and our exercise price (K) is 300, the payoff of
our put is K - S ➔ 300 – 310 = 0. If the price of 1 AAPL stock is 290, it is below the exercise price and
our payoff is 300 – 290 = 0.
The value of a long put option (P) can thus be formulated as P = max(K – S, 0).
Tip: learn the formulas for a long put and long call option by heart from the very start, it will make
things a lot less complex further on! During the exam people still mix up both formulas though.
Short calls and puts
Knowing
Fu what long puts and calls are makes learning short puts and calls a lot easier. They are the exact
opposite. The value of a short call is simply the value of a long call with a ‘-‘ sign in front of it. So C =
max(S – K, 0) now becomes C = -max(S – K, 0). The same applies to a short put: P = max(K – S, 0)
now becomes P = -max(K – S, 0). So where a long call/put start making money, a short call/put loses
money.
Suppose an investor buys a call (so it takes a long position) with an exercise price (K) of €300 on AAPL
stock of which the underlying price (S) is also €300 (the call is therefore at-the-money). If the price
moves up, let’s say it is €320, the investor makes C = max(S – K, 0) ➔ C = max(320 – 300, 0) = €20.
Suppose the price doesn’t go up and it is €280. The long call option’s payoff is now C = max(S – K, 0)
➔ C = max(280 – 300, 0) = €0. However, as stated before, the investor does lose money! It had to pay
the premium to the option writer/seller – the person that has a short position in the long contract!
The one who sells the call option is short and receives C = -max(S – K, 0) ➔ C = -max(280 – 300, 0) =
€0 but receives the premium from the investor that was long and actually makes money! Had the price
gone up to €320 however, the short call’s payoff would have been C = -max(S – K, 0) ➔ C = -max(320
– 300, 0) = -€20. So the investor actually loses 20 (notice the ‘-‘ sign!), but given that it receives the
premium it could still make money if the premium exceeds the loss of €20. This works the same way
for short puts.
20.3 Option payoff plots
Here’s a quick note before looking at the payoff plots of options in detail: the book uses payoff plots
which don’t include premia. This makes things a lot more confusing in my opinion, since the exercises
on the exam require you to incorporate the knowledge that options have premia. Here’s what I mean:
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,The diagram on the left depicts the payoff diagram of a long call which includes the premium. The y-
axis shows the profits (P&L) and the x-axis shows the price (S) of the underlying asset. The long call
starts off with a negative profit of -100 on the left-hand side due to the premium which the investor pays.
When the price of the asset (S) reaches the strike price (K) of 25, the call starts to “make” money.
Remember that when C = max(S – K, 0) is large enough such that it exceeds the premium the investor
has paid, it finally has a positive P&L (its breakeven point is somewhere between 26 and 27). From that
point on, any increase in the price of the underlying asset equals profit.
The book however uses the simple diagram on the right to show the payoff of a long call. This diagram
does not incorporate the premium that is paid to the investor, which makes it seem as if the investor
either makes money when the price goes up, and NEVER loses money when the price goes down.
I will use the payoff plots like the first one, in order to make you fully understand the way option
diagrams can be interpreted.
Long call and long put payoff diagram
As mentioned above, this is the payoff plot of a
long call for any given asset. The y-axis always
shows the profit and losses, and the x-axis the
price of the underlying. Remember the formula
that describes the value of a long call: C = max(S
– K, 0). If K = $40 here and S happens to be $50,
the payoff is C = max(50 – 40, 0) = $10 (Given
that an option contract consists of 100 options
the investor makes $10 x 100 = $1000. Total
profit thus equals $1000 - $200 = $800).
If the price falls below K to $30, the investor
makes C = max(30 – 40, 0) = $0. However, the
plot shows that the investor actually loses
money since it pays a premium to the option seller of $200 and its net profit is thus -$200.
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, This payoff diagram depicts the payoff plot of a
long put. The general formula for the value of a
long put is P = max(K – S, 0). If the price falls
below the K of $40, the investor starts to make
money. If S = $30, the investor earns P = max(40
– 30, 0) = $10 ($10 x 100 = $1000).
In addition, if S increases to $50, the investor
loses. The payoff is P = max(40 – 50, 0) = 0.
However, it still pays the premium of $200 and
its net profit is -$200.
To summarize, the value of a long call increases
as long as the price of the underlying (S)
increases. The value of a long put increases as the price of the underlying decreases.
Short call and short put payoff diagram
The option payoff diagram of a short call looks
like the one on the left. Remember the general
formula for the value of a short call: C = -max(S
– K, 0). Here, K = $50. The investor that is
shorting the call is losing money as S increases
to be above 50. If S is $55, the investor makes
C = -max(55 – 50, 0) = -$5. Hence, if S
increases in value, the investor that has a
position in a short call starts to lose money. The
net P&L would be (-$5 x 100 = -$500 + $300 =
-$200).
If S falls below K, suppose S is $45, the investor
earns C = -max(45 – 50, 0) = -$0. However, it
still earns the premium of $300.
The diagram on the left depicts the opposite
once again: the payoff plot of a short put.
Remember that the general formula for the
value of a short put was P = -max(K – S, 0).
Here, K = $5200. If S falls below K, suppose it
is $5100, the investor loses: P = -max(5200 –
5100, 0) = -$100 (Net P&L would be -$100 x
100 = -$10,000 + $3500 = -$6500).
If S however is above K, suppose S is $5400,
the payoff of a short put is P = -max(5100 –
5400, 0) = $0, but the option seller still earns
the premium of $3500.
To summarize, the value of a short call
decreases as S increases. The value of a short put decreases as S decreases.
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, 20.4 Combinations of options
As mentioned before, options do not only allow investors to speculate on the price of the underlying to
go up or down, but also on the volatility of underlying. Betting on the volatility of the underlying can
be done by combining options. There are 4 prominent combinations that you have to know for your
exam:
Straddle
The straddle is a simple combination of a put and call with the same exercise price (K) and maturity (T).
A long straddle therefore is the combination of a long put and a long call that both have the same K and
T. A short straddle is thus a combination of a short put and a short call with the same K and T.
Long straddle = C(K, T) + P(K, T). K and T represent the same values for both the (C)all and (P)ut.
Short straddle = -C(K, T) + -P(K, T).
When would you go short on an at-the-money straddle? When volatility is low! Why? Assume that S =
40 and since that the option is at-the-money, so K = 40 as well. Both have the same maturity. Since we
go short on both a call and a put, we receive a premia for both. Suppose that S decreases by a little bit
because the volatility of the stock is very low and is $39.5 at expiration, the short call makes C = -
max(39.5 – 40, 0) = 0 and the short put loses P = -max(40 – 39.5, 0) = -0.5. The investor only loses 0.5,
but given that it has received a premia for both the put and call of $400, the investor actually makes
money.
Check out the short straddle payoff diagram on the left.
If volatility is high, there is a large chance that the price
will move away from 40, either towards 30 or 50, and
the closer S moves towards the 30 or 50, the more the
investor loses. In fact, if you look closely, the investor
breaks even at 35 and 45. If the price stays between 35
and 45 the investor makes a profit. Hence, low
volatility is ideal to take a short position in a straddle.
A long straddle would be ideal in the opposite situation:
where volatility is high.
The payoff of a long straddle is thus: max(S – K, 0) +
max(K – S, 0). The payoff of a short straddle is -max(S – K, 0) – max(K – S, 0).
Strangle
A strangle is once again a combination of both and a put and call. The difference is that the put has a
lower K than the call. Both still have the same maturity.
Long strangle = P(K1, T) + C(K2, T), K1 < K2. The strike price of the put (K1) is smaller than the
strike price of the call (K2).
Short strangle = -P(K1, T) – C(K2, T), K1 < K2.
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