STOCHASTIC METHODS IN FINANCE 2021–22 STAT0013
Exercises 3 – Binomial Model
1. A stock price is currently $40. It is known that at the end of one month it will be either $42 or $38. The risk-free interest rate is 8% per annum with continuous compounding. Calculate the value of a one-month European call option with a strike price of $39 using
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(a) a risk-neutral approach
(b) a replicating portfolio approach.
2. A stock price is currently $50. It is known that at the end of six months it will be either $45 or $55. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a six- month European put option with strike price of $50? Use a risk-neutral approach.
3. A stock price is currently £100. Over the next two six-month periods it is expected to go up by 10% or down by 10%. The risk free rate is 8% per annum with continuous compounding. What is the value of a one-year European call option with strike price £100?
4. A stock price is currently £25. It is known that at the end of two months it will be either £23 or £27. The risk-free rate is 10% per annum with continuous compounding. Suppose ST is the stock price at the end of two months. What is the value of a derivative that pays ST2 at the end of two months?
5. A stock price is currently £50. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free rate is 5% per annum with continuous compounding.
(a) Calculate the value of a six-month European call option with strike price £51.
(b) Calculatethevalueofasix-monthEuropeanputoptionwithstrike price £51.
(c) Verify that put call parity holds.
(d) When, if ever, would it be worth exercising a six-month American
put option with strike price £51?
(e) What is the value today of the six-month American put option
with strike price £51?
(f) What is the value today of the six-month American call option
with strike price £51?
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