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Seminar: Autumn 2006
Stanford Financial Mathematics Seminar Schedule
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| Game Theoretic Approach for Option Pricing |
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Ilan Kremer (Stanford, GSB)
We study the link between the game theoretic notion of approachability or “regret minimization” and robust option pricing. We demonstrate how trading strategies that are based on approachability and minimize regret over finite horizon also imply robust upper bounds for the prices of European call options. These bounds are based on no arbitrage and are robust in that they require only minimal assumptions regarding the stock price process. We then focus on the optimal bounds and solve for the optimal volatility-based bounds in closed-form, which in turn implies the optimal regret-minimizing trading strategy. The bounds we obtain seem to be empirically relevant as they resemble option price patterns observed in practice.
Joint work with Peter M. DeMarzo and Yishay Mansour†
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| Hedging Variance Options on Continuous Semimartingales |
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Roger Lee (Chicago)
Variance swaps, which pay the realized variance of [the returns on]
an underlying price process, have become a leading tool for managing
exposure to volatility risk. Variance options -- calls and puts on
realized variance -- allow portfolio managers greater control over
volatility risk exposure, but present greater hedging difficulties
to the dealer.
Assuming only that the underlier is a positive continuous
semimartingale, we model-independently superreplicate and
subreplicate variance options and forward-starting variance options,
by dynamically trading the underlier, and statically holding
European options.
In contrast to my August talk (on lower bounds),
this one focuses on upper bounds.
Joint with Peter Carr.
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| Volatility and Correlation Exposure in the Credit Markets |
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Jacky Lee (Credit Suisse)
We discuss credit volatility supply and demand in the single name and
credit index markets. We study the interplay of volatility and correlation
and effective tranche hedging. We conclude with the examination of spread
dispersion effects in several hedging methods and a discussion of the
non-uniqueness of tranche deltas.
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| Sherlock Trader: Takeover Sleuth |
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Mike Lipkin (Katama Trading, LLC, American Stock Exchange, NY)
Rumors and leaks of takeovers have a profound impact on the options markets and give the astute observer a critical clue to their potential occurrence.
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