Options with Extreme Strikes
نویسندگان
چکیده
منابع مشابه
Options with Extreme Strikes
In this short paper, we study the asymptotics for the price of call options for very large strikes and put options for very small strikes. The stock price is assumed to follow the Black–Scholes models. We analyze European, Asian, American, Parisian and perpetual options and conclude that the tail asymptotics for these option types fall into four scenarios.
متن کاملThe Moment Formula for Implied Volatility at Extreme Strikes
Consider options on a nonnegative underlying random variable with arbitrary distribution. In the absence of arbitrage, we show that at any maturity T , the large-strike tail of the Black-Scholes implied volatility skew is bounded by the square root of 2|x|/T , where x is log-moneyness. The smallest coefficient that can replace the 2 depends only on the number of finite moments in the underlying...
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The course consists of two lectures (1.5 hours each). It will be explained in the lectures how the implied volatility (the smile) behaves at large strikes. We will discuss and prove several known results describing the smile asymptotics. There results include Lee’s moment formulas, the tail-wing formula of Benaim and Friz, and the asymptotic formulas with error estimates due to the author. The ...
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In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee’s moment formulas for the implied volatility and the tail-wing formulas due to Benaim and Friz. In addition, we analyze Pareto-type tails of stock price distributions in uncorrelated Hull-White, Stein-Stein, and Hest...
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ژورنال
عنوان ژورنال: Risks
سال: 2015
ISSN: 2227-9091
DOI: 10.3390/risks3030234