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RSK4805 Assignment 3 2023 (ANSWERS)

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RSK4805 Assignment 3 2023 (ANSWERS) Question 1 (25 marks) 1.1 An analyst for LevelUP gathered the following information regarding a futures contract: • Current spot-market price of R60 • The continuous compounded risk-free interest rate of 8.5% per annum • The actual futures price...

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  • July 19, 2023
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, QUESTION 1.


1.1 To calculate the price of the future contract for delivery in six months, we can use the
formula for the cost of carry model:


Future price = Spot price * e^(r * t)


Where:
Spot price = R60 (current spot-market price)
r = Risk-free interest rate = 8.5% per annum = 0.085
t = Time to delivery in years = 6 months / 12 months = 0.5


Future price = R60 * e^(0.085 * 0.5)
Future price = R60 * e^0.0425
Future price = R60 * 1.043402
Future price = R62.0041


The calculated price of the future contract for delivery in six months is R62.0041.


To determine whether the contract is overpriced, underpriced, or correctly priced, we
compare the calculated price (R62.0041) with the actual futures price (R61). Since the
calculated price is higher than the actual futures price, the contract is underpriced.


1.2 To estimate the impact of a market shock on the value of the delta-neutral portfolio, we
need to consider both the gamma and vega.


Gamma represents the change in the portfolio's delta for a given change in the underlying
asset price. In this case, the gamma is 55, indicating that for every R1 change in the
underlying asset price, the portfolio's delta will change by 55.


Vega represents the change in the portfolio's value for a 1% change in the underlying
asset's volatility. In this case, the vega is 27, given as a percentage. To calculate the
actual value change due to a 5% increase in volatility, we multiply the vega by the
percentage change:

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