In options markets where there is a significant or persis- tent volatility smile, implied tree models can ensure the consistency of exotic options prices with…

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Most real-world barrier options have no analytic solutions, either because the barrier structure is complex or because of volatility skews in the market. Numerical solutions…

Comments closedNovember 1994 – A one-factor convertible model now used by many hedge funds. Convertible bonds are derivative securities; they contain options on the underlying common…

Comments closedThe Journal of Derivatives, 2-4 Summer 1995, pp. 78-95 This paper presents a method for replicating or hedging a target stock option with a portfolio…

Comments closedgs-volatility_smile RISK, 7-2 Feb.1994, pp. 139-145, pp. 32-39 The market implied volatilities of stock index options often have a skewed structure, commonly called “the volatility…

Comments closedTo me, outperformance options1 are especially interesting because of the alternating layers of complexity and simplicity you discover as you probe more deeply into their…

Comments closedThis article describes a model of interest rates that can be used to value any interest-rate-sensitive security. In explaining how it works, we concentrate on…

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