# Question: A European shout option is an option for which the

A European shout option is an option for which the payoff at expiration is max(0, S − K, G − K), where G is the price at which you shouted. (Suppose you have an XYZ shout call with a strike price of $100. Today XYZ is $130. If you shout at $130, you are guaranteed a payoff of max($30, ST − $130) at expiration.) You can only shout once, irrevocably.

a. Demonstrate that shouting at some arbitrary priceG>K is better than never shouting.

b. Compare qualitatively the value of a shout option to (i) a lookback option (which pays max[0, ST − K], where ST is the greatest stock price over the life of the option) and (ii) a ladder option (which pays max(0, S − K, L − K) if the underlying hits the value L at some point over the life of the option).

c. Explain how to value this option binomially.

a. Demonstrate that shouting at some arbitrary priceG>K is better than never shouting.

b. Compare qualitatively the value of a shout option to (i) a lookback option (which pays max[0, ST − K], where ST is the greatest stock price over the life of the option) and (ii) a ladder option (which pays max(0, S − K, L − K) if the underlying hits the value L at some point over the life of the option).

c. Explain how to value this option binomially.

## Answer to relevant Questions

Consider the Level 3 outperformance option with a multiplier, discussed in Section 16.2. This can be valued binomially using the single state variable SLevel 3/SS&P, and multiplying the resulting value by SS&P. a. Compute ...Assume that S = $45, K = $40, r = 0.05, δ = 0.02, and σ = 0.30. Using the up rebate formula (equation (23.21)), find the value of H that maximizes (H − K) × UR(S, σ, r , T , δ), for T = 1, 10, 100, 1000, and 10,000. ...Compute January 12 2004 implied volatilities using the average of the bid and ask prices for IBM options expiring February 21 (use the Black-Scholes implied volatility function). Compare your answers to those in the previous ...Using the CEV option pricing model, set β = 1and generate option prices for strikes from 60 to 140, in increments of 5, for times to maturity of 0.25, 0.5, 1.0, and 2.0. Plot the resulting implied volatilities. (This should ...Compute January 12 2004 bid and ask volatilities (using the Black-Scholes implied volatility function) for IBM options expiring January 17. For which options are you unable to compute a plausible implied volatility? Why?Post your question