April 2010
Beginner
2224 pages
100h 29m
English
Content preview from Encyclopedia of Quantitative Finance, IV Volume Set
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ICAPM see Capital Asset Pricing Model
Implied Volatility: Large Strike Asymptotics
Let St be the price of a risky asset at time t 
[0, T] and Bt = B (t, T) the time-t value of one monetary unit received at time T. Assuming suitable no-arbitrage conditions, there exists a probability measure 
, called the (T -forward) pricing measure, under which the Bt-discounted asset price
is a martingale and so are Bt-discounted time-t option prices, such as Ct/B (t, T), where Ct denotes the time-t value of a European call option with maturity T and payoff (ST − K)+. With focus on t = 0 and writing C instead of C0, we have
Let us remark that in the case of deterministic interest rates r (·), one can rewrite this asa
If we now make the assumption that there exists σ > 0, the Black–Scholes volatility
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