Brief Summary: Finance 2 Thomas Konings
Contents
Week 1: Derivatives, Forwards/Futures, Call/Put Options ..................................................................... 1
Week 2: Futures I, Compounding, Pricing Forwards, Currency Forward................................................ 1
Week 3: Futures II: Commodity, Hedging, Interest Rate Futures ........................................................... 2
Week 4: Options I: Put-Call Parity, Early American, Binomial Pricing..................................................... 3
Week 5: Options II, Black-Scholes, Option Greeks.................................................................................. 3
Week 6: Implied Volatility, Perpetual Options, Real Options ................................................................. 4
Week 1: Derivatives, Forwards/Futures, Call/Put Options
Derivative: payoff based on another asset’s price, introduction of them results in increased price risk
Uses of derivatives: 1. Risk Management 2. Speculation (investment)
3. Reduced transaction costs (sometimes) 4. Regulatory arbitrage (circumvent restriction/taxes)
Applications: hedge currency exposure, lock in prices, accounting: manage interest and default risk
End users: corporations, investment managers, investors Intermediaries: market-makers, traders
Observers: regulators, researchers → Exchange: buy/sell clearinghouse = counterparty
Over-the-Counter (OTC): bypass exchange (public and regulated) → not easy to observe
Forward contract: binding agreement to buy/sell asset in future for price determined today.
→ Futures: same but institutionally/exchanges/standardized (features/quantity, delivery, price)
Payoff forward contract: Long forward: Spot Price at Expiration – Forward Price (𝑆𝑇 − 𝐹0 )
Short forward: Forward – Spot at Expiration (𝐹0 − 𝑆𝑇 )
Call options: non-binding agreement (right) to buy asset in the future at price determined today
→ Preserves upside potential, eliminates the downside (not exercised) Strike/exercise price: 𝐾
Exercise style: (1) European [only at expiration] (2) American [any time before expiration]
(3) Bermudan [only during specific periods]
Payoff Call Option: max(0, 𝑆𝑇 − 𝐾) Profit: 𝑝𝑎𝑦𝑜𝑓𝑓 − 𝐹𝑉𝑜𝑓𝑂𝑝𝑡𝑖𝑜𝑛𝑃𝑟𝑒𝑚𝑖𝑢𝑚(𝐶)
“write a call” → Payoff: −max(0, 𝑆𝑇 − 𝐾) Profit: 𝑝𝑎𝑦𝑜𝑓𝑓 + 𝐹𝑉𝑜𝑓𝑂𝑝𝑡𝑖𝑜𝑛𝑃𝑟𝑒𝑚𝑖𝑢𝑚(𝐶)
Put options: right to sell and asset in the future at price determined today (“writer” has to buy)
Payoff: max(0, 𝐾 − 𝑆𝑇 ) [option allows you to sell for more than the spot price]
Profit: 𝑝𝑎𝑦𝑜𝑓𝑓 − 𝐹𝑉𝑜𝑓𝑂𝑝𝑡𝑖𝑜𝑛𝑃𝑟𝑒𝑚𝑖𝑢𝑚(𝑃)
Written/short put: −max(0, 𝐾 − 𝑆𝑇 ) Profit: 𝑝𝑎𝑦𝑜𝑓𝑓 + 𝐹𝑉𝑜𝑓𝑂𝑝𝑡𝑖𝑜𝑛𝑃𝑟𝑒𝑚𝑖𝑢𝑚(𝑃)
Moneyness: “in” → 𝑝𝑎𝑦𝑜𝑓𝑓 > 0 “at” → 𝑝𝑎𝑦𝑜𝑓𝑓 = 0 “out” → 𝑝𝑎𝑦𝑜𝑓𝑓 < 0
Week 2: Futures I, Compounding, Pricing Forwards, Currency Forward
𝑟𝑡 (𝑡1 , 𝑡2 ): forward rate 𝑡1 to 𝑡2 as observed at 𝑡 → so 𝑟0 (0, 𝑡2 ) = zero/spot rate
𝑝𝑡0 (𝑡1 , 𝑡2 ): price bond quoted at t=0, purchased at 𝑡1 maturing 𝑡2 YTM: money gained by bond
𝑟(0,1) 𝑛
Compounding: when compounding 𝐴𝑛 times per year: 𝐴 ∗ (1 + 𝑛
) cont: 𝑒 𝑟(0,1)𝑇
𝑟𝑐
𝑟
Conversion: 𝑟𝑐 = 𝑛 ∗ ln(1 + 𝑛 ) 𝑟𝑛 = 𝑛 ∗ (𝑒 𝑛 − 1)
𝑛
𝐶𝑇
Zero coupon bonds (ZCB): pays 𝐶𝑇 at 𝑇: discrete: 𝐵(0, 𝑇) = 𝑟(0,𝑇) 𝑛𝑇
cont: 𝐵(0, 𝑇) = 𝐶𝑇 𝑒 −𝑟(0,𝑇)𝑇
(1+ )
𝑛
© Thomas Konings – 2020 1
