European Options on Forward and Futures Contracts
This chapter continues our analysis of standard instruments found on the balance sheet of large financial institutions as we continue with our objective of establishing a unified measure of interest rate risk, market risk, liquidity risk, and credit risk. In order to value the Jarrow-Merton put option proposed in Chapter 1 as the best measure of total risk, we need a methodology for valuation and for simulation of cash flows and values at many future dates. As in Chapter 22, we need this capability for European options on forward and futures contracts for three reasons:
- To understand correct hedging amounts from a shareholder value-added perspective, as discussed in the early chapters of this book
- To meet the requirements of constantly evolving accounting standards for hedging
- To meet the requirements of regulatory capital calculations like Basel II, Basel III, and Solvency II
This chapter combines the valuation formulas for futures and forwards from Chapter 22 and the options approach from Chapter 21. As in Chapters 21 and 22, we use the three-factor Heath, Jarrow, and Morton (HJM) framework to value options on forwards and futures. We remind the reader that Chapter 3 illustrated the need for an interest rate model with 5 to 10 driving risk factors. We use the three-factor HJM model from Chapter 9 for expositional purposes. In the first edition of this book, we showed in detail how the one-factor Vasicek model can ...