Metaphors, Models & Theories When I was in grade school we used to build model airplanes out of kits. The frame was made out precut…
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Investors in equity options experience two problems that compound each other. In contrast to fixed-income and currency markets, there are thousands of underlyers and tens…
Comments closedrisk-regimes_of_volatility Since the 1987 stock market crash, the S&P 500 index options market has displayed a persistent implied volatil- ity skew. How should the skew…
Comments closedVolatility swaps are forward contracts on future realized stock volatility. Variance swaps are similar contracts on vari- ance, the square of future volatility. Both of…
Comments closedThe insight behind the Black-Scholes formula for options valuation is the recognition that, if you know the future volatility of a stock, you can replicate…
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Comments closedScientific American: Feature Article: A Calculus of Risk: May 1998
Comments closedThis note outlines a methodology for hedging and trading index volatilities. In the bond world, forward rates are the arbitrage-free interest rates at future times…
Comments closedBarrier options are extensions of standard stock options. Standard calls and puts have payoffs that dependon one market level: the strike. Barrier options have payoffs…
Comments closedjpm-reflections_on_fischer I first met Fischer in 1986, several months after I came to work in Fixed Income Research at Goldman, Sachs & Co. I knew…
Comments closedI’m very pleased and honored to be here and to say a few words about Fischer on this occasion. But, both for my sake and…
Comments closedPublished in RISK, 10(6) Jun. 1997, p. 75 I often interview job candidates with degrees in science or finance. I `m always glad if they…
Comments closedIf you examine the structure of listed index options prices through the prism of the implied tree model, you observe the local volatility surface of…
Comments closedModel Risk – FILL
Comments closedIn options markets where there is a significant or persis- tent volatility smile, implied tree models can ensure the consistency of exotic options prices with…
Comments closedMost 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…
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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…
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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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