Derivatives: Option and Binomial Tree
FINM3405 Derivatives & Risk Management Tutorial 6 Reference Material
Lecture 8 (class notes and lecture slides)
Tutorial Questions
Question 1 A stock is currently priced at $20. In any given 4-month period, stock price will either go up by 18.91% or down by 15.9%.1 The riskless rate of interest is 4% per annum continuously compounded. A European-style call option is written on this stock with a $12 strike price and 8 months to expiry. a) b) c) d) Use the delta-hedging approach to price this call option. Use the risk-neutral valuation method to price this call option. Work recursively back through the Binomial tree, calculating the call option price at each node. Check that the option price at each node matches that calculated in part a. Again use the risk-neutral method to value this call option, but this time do not work back recursively. Rather, focus on the terminal distribution of stock price (and the number of paths which lead to each terminal stock price). Assume a European-style put option is written on this stock. It has 8 months to expiry and a $25 strike price. Focusing on the terminal distribution of stock price, value this put option.
Question 2
[European v. American Put Option]
A stock is currently priced at $100. In any given 3-month period, stock price will either go up by 13.31% or down by 11.75%. The riskless rate of interest is 5% per annum continuously compounded. A put option is written on this stock with a $110 strike price and 9 months to expiry. a) b) c) Assume the put option is European-style. Calculate the current value of the put. Use whatever method you like, but it will be quickest to focus on the terminal distribution of stock price. Now assume it is an American-style put option. Calculate the current value of the put option. Now assume that the above put option is Bermudan-style which can be exercised at t = 3 months and at t = 9 months. Use the risk-neutral approach to calculate the current value of this put option.
Lecture 8 (class notes and lecture slides)
Tutorial Questions
Question 1 A stock is currently priced at $20. In any given 4-month period, stock price will either go up by 18.91% or down by 15.9%.1 The riskless rate of interest is 4% per annum continuously compounded. A European-style call option is written on this stock with a $12 strike price and 8 months to expiry. a) b) c) d) Use the delta-hedging approach to price this call option. Use the risk-neutral valuation method to price this call option. Work recursively back through the Binomial tree, calculating the call option price at each node. Check that the option price at each node matches that calculated in part a. Again use the risk-neutral method to value this call option, but this time do not work back recursively. Rather, focus on the terminal distribution of stock price (and the number of paths which lead to each terminal stock price). Assume a European-style put option is written on this stock. It has 8 months to expiry and a $25 strike price. Focusing on the terminal distribution of stock price, value this put option.
Question 2
[European v. American Put Option]
A stock is currently priced at $100. In any given 3-month period, stock price will either go up by 13.31% or down by 11.75%. The riskless rate of interest is 5% per annum continuously compounded. A put option is written on this stock with a $110 strike price and 9 months to expiry. a) b) c) Assume the put option is European-style. Calculate the current value of the put. Use whatever method you like, but it will be quickest to focus on the terminal distribution of stock price. Now assume it is an American-style put option. Calculate the current value of the put option. Now assume that the above put option is Bermudan-style which can be exercised at t = 3 months and at t = 9 months. Use the risk-neutral approach to calculate the current value of this put option.