American and European options in multi-factor jump-diffusion models,near expiry |
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Authors: | Sergei Levendorskiǐ |
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Institution: | (1) Department of Economics, The University of Texas at Austin, 1 University Station C3100, Austin, TX 78712-0301, USA |
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Abstract: | We derive a general formula for the time decay θ for out-of-the-money European options on stocks and bonds at expiry, in terms of the density of jumps F(x,dy) and the payoff g
+: −θ(x)=∫
g(x+y)+
F(x,dy). Explicit formulas are derived for the standard put and call options, exchange options in stochastic volatility and local
volatility models, and options on bonds in ATSMs. Using these formulas, we show that in the presence of jumps, the limit of
the no-exercise region for the American option with the payoff (−g)+ as time to expiry τ tends to 0 may be larger than in the pure Gaussian case. In particular, for many families of non-Gaussian processes used
in empirical studies of financial markets, the early exercise boundary for the American put without dividends is separated
from the strike price by a nonvanishing margin on the interval 0,T), where T is the maturity date.
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Keywords: | Critical price near expiry American puts Calls Exchange options Bond options European options near expiry Jump-diffusions ATSM QTSM |
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