### Which Free Lunch Would You Like Today, Sir?: Delta Hedging, Volatility Arbitrage and Optimal Portfolios

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In the following, I will say what the smile problem is, and I am not sure everyone will follow me. This is how deeply and how long I’ve been thinking about the smile problem. I’ve […]

The 1977 science fiction movie Close Encounters of the Third Kind was written and directed by Steven Spielberg. The title is derived from the classification by Hynek for close encounters with aliens, in which the […]

How do I love thee? Let me count the ways. I love thee to the depth and breadth and height My soul can reach, when feeling out of sight. . . I love thee with […]

In this article we apply the ADE method to a number of partial differential equations in option pricing using one-factor models (Black–Scholes, local volatility, uncertain volatility). We first give an introduction to ADE. We discuss […]

Even if you started out clueless about the volatility σ , given a good enough measuring stick and fast enough hands you ought to be able to measure it quickly and accurately. In practice you […]

Word and concept Implied volatility is not just a word or a concept. As a word, what is implied by implied volatility – what “implied volatility” means – is the value of the Brownian diffusion […]

The purpose of this article is to introduce the properties of variance swaps, and give insights into the hedging and valuation of these instruments from the particular lens of an option trader. Section 1 gives […]

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