# Question

Suppose that S and Q follow equations (20.36) and (20.37). Derive the value of a claim paying S(T )aQ(T )b by each of the following methods:

a. Compute the expected value of the claim and discounting at an appropriate rate.

b. Compute the lease rate and substituting this into the formula for the forward price.

a. Compute the expected value of the claim and discounting at an appropriate rate.

b. Compute the lease rate and substituting this into the formula for the forward price.

## Answer to relevant Questions

Assume that one stock follows the process dS/S = αdt + σdZ (20.44) Another stock follows the process dQ/Q = αQdt + σdZ + dq1+ dq2 (20.45) a. If there were no jump terms (i.e., λ1 = λ2 = 0), what would be the relation ...Suppose that S follows equation (20.36) and Q follows equation (20.37). Use Itˆo’s Lemma to find the process followed by ln(SQ). What is the value of a claim paying Q(T )−1S(T )? Check your answer using Proposition 20.4. Use the answers to the previous two problems to verify that the Black-Scholes formula, equation (12.1), satisfies the Black-Scholes equation. Verify that the boundary condition V [S(T), T ]= max[0, S(T ) − K] is satisfied. Warren Buffett stated in the 2009 Letter to Shareholders: "Our derivatives dealings require our counterparties to make payments to us when contracts are initiated. Berkshire therefore always holds the money, which leaves us ...Post your question

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