Chapter

Stock and Currency Derivatives When Interest Rates are Stochastic

Claus Munk

in Fixed Income Modelling

Published in print June 2011 | ISBN: 9780199575084
Published online September 2011 | e-ISBN: 9780191728648 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199575084.003.0015
Stock and Currency Derivatives When Interest Rates are Stochastic

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Previous chapters have focused on the pricing of bonds and assets with payments determined by future interest rates. This chapter studies the impact of the shape and the dynamics of the yield curve on the prices of securities with payments that depend on other random variables. The present value of a security involves the discounting of the future payments, and the appropriate discount factors depend on the interest rate uncertainty as well as the correlations between interest rates and the random variables that determine the payments of the security. Particular focus is on the pricing of stock options allowing for stochastic interest rates — in contrast to the classic Black-Scholes-Merton model. General results on the pricing of options on forwards or futures are derived. The pricing of forwards, futures, and European options on a foreign currency is also discussed.

Keywords: stock option; option on forward; Gaussian model; currency forward; currency futures; currency option

Chapter.  9601 words. 

Subjects: Financial Markets

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