In this chapter, a diversion is taken from the book’s primary focus on callable mortgage bonds. It shows how to value cash-settled swaptions via the replication formula normally used for valuing options of the European type, in which the payoff is given as a two-time differentiable function of the underlying, in this case, the swap rate. A section showing how to perform exact calculations of sensitivity key figures in a stochastic volatility model is also presented. This chapter has been included to demonstrate how modern mathematical finance is being used in practice, and it is a continuation of Chap. 9 in the sense that both chapters use a terminal swap rate model to calculate values of interest rate derivatives.

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Cash-Settled Swaptions

  • Niels Rom

摘要

In this chapter, a diversion is taken from the book’s primary focus on callable mortgage bonds. It shows how to value cash-settled swaptions via the replication formula normally used for valuing options of the European type, in which the payoff is given as a two-time differentiable function of the underlying, in this case, the swap rate. A section showing how to perform exact calculations of sensitivity key figures in a stochastic volatility model is also presented. This chapter has been included to demonstrate how modern mathematical finance is being used in practice, and it is a continuation of Chap. 9 in the sense that both chapters use a terminal swap rate model to calculate values of interest rate derivatives.