Problem (ii)

Explain the risk neutral and the no-arbitrage valuation approaches to valuing an option using a one-step binomial tree.

Problem iii

Consider a European put option on a non-dividend-paying stock where the stock price is 2.50, the strike price is 2.50, the risk-free rate of interest is 2% per annum, the volatility is 20% per annum, and the time to maturity is six months.

1. Calculate u, d and p for a two time-step binomial tree
2. Value the option using a two time-step binomial tree.
3. Calculate and interpret the delta and gamma option price sensitivities at the second time step

[Final exam, 2017]

Problem v

Consider a 4-month European put option on a share where the current share price is 20 pence, the exercise price is 22 pence, the risk-free interest rate is 2.25% per annum, and the volatility of the underlying share is 25% per annum.

(i) Use a two-time-step tree to calculate the price of the European put option.

(ii) If the put option was American, with all other characteristics the same, what would be the price of the option?

(November Class Test 2020)

Problem iv Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is six months. a. Calculate u, d, and p for a two step tree b. Value the option using a two step tree. c. Verify that Deriva Gem gives the same answer d. Use Deriva Gem to value the option with 5, 10, 20 time steps. Problem iv Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is six months. a. Calculate u, d, and p for a two step tree b. Value the option using a two step tree. c. Verify that Deriva Gem gives the same answer d. Use Deriva Gem to value the option with 5, 10, 20 time steps