# Question: Refer to Figure 19 2 a Verify that the price of a

Refer to Figure 19.2.

a. Verify that the price of a European put option is $0.0564.

b. Verify that the price of an American put option is $0.1144. Be sure to allow for the possibility of exercise at time 0.

a. Verify that the price of a European put option is $0.0564.

b. Verify that the price of an American put option is $0.1144. Be sure to allow for the possibility of exercise at time 0.

## Answer to relevant Questions

Assume S0 = $50, r = 0.05, σ = 0.50, and δ = 0. The Black-Scholes price for a 2-year at-the-money put is $10.906. Suppose that the stock price is lognormal but can also jump, with the number of jumps Poisson-distributed. ...Suppose S0 = 100, r = 0.06, σS = 0.4 and δ = 0. Use Monte Carlo to compute prices for claims that pay the following: a. S21 b.√S1 c. S1-2 Suppose that S1 follows equation (20.26) with δ = 0. Consider an asset that follows the process dS2 = α2S2 dt − σ2S2 dZ Show that (α1 − r)/σ1=−(α2 − r)/σ2. S1 and S2 that eliminates risk.) Suppose S(0) = $100, r = 0.06, σS = 0.4, and δ = 0. Use equation (20.32) to compute prices for claims that pay the following: a. S2 b.√S c. S−2 Compare your answers to the answers you obtained to Problem 19.6. Verify that ASaeγ t satisfies the Black-Scholes PDE forPost your question