TY - JOUR
T1 - Volatility risk structure for options depending on extrema
AU - Nakatsu, Tomonori
N1 - Publisher Copyright:
© 2017 Infopro Digital Risk (IP) Limited.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/12
Y1 - 2017/12
N2 - In this paper, we give a decomposition formula to calculate the vega index (sensitivity with respect to changes in volatility) for options with prices that depend on the extrema (maximum or minimum) and terminal value of the underlying stock price; this is assumed to follow a one-dimensional perturbed diffusion process. As a numerical application, we compute the vega index for lookback, European and up-in call options under the Black-Scholes model perturbed with a constant elasticity of variance modeltype perturbation. We compare these values with the standard nonperturbed Black-Scholes model, which, interestingly, turn out to be very different.
AB - In this paper, we give a decomposition formula to calculate the vega index (sensitivity with respect to changes in volatility) for options with prices that depend on the extrema (maximum or minimum) and terminal value of the underlying stock price; this is assumed to follow a one-dimensional perturbed diffusion process. As a numerical application, we compute the vega index for lookback, European and up-in call options under the Black-Scholes model perturbed with a constant elasticity of variance modeltype perturbation. We compare these values with the standard nonperturbed Black-Scholes model, which, interestingly, turn out to be very different.
KW - Barrier option
KW - Lookback option
KW - Malliavin calculus
KW - Stochastic differential equation
KW - Vega
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U2 - 10.21314/JCF.2017.334
DO - 10.21314/JCF.2017.334
M3 - Article
AN - SCOPUS:85037598057
VL - 21
SP - 105
EP - 122
JO - Journal of Computational Finance
JF - Journal of Computational Finance
SN - 1460-1559
IS - 3
ER -