We propose an analytically tractable local volatility model for asset price dynamics leading to volatility smile/skew and fatter-tailed probability distribution. The proposed local volatility model is based on stochastic process of hyperbolic-sine type. We derive the transition probability density function for hyperbolic-sine model and justify that this function has delta function terminal condition at initial time. We compare the probability density functions in Black-Scholes and hyperbolic-sine models to demonstrate that the probability distribution in hyperbolic sine model has some features of fat-tailed distributions. Risk neutral valuation technique is applied to find explicit valuation formula for European call option price in hyperbolic-sine model. In hyperbolic-sine model European call option is more valuable than an identical option in Black-Scholes model for ATM options. We verify that in hyperbolic-sine model Breeden-Litzenberger formula (relation between European call option price and probability density function) holds true. We also examine that Dupire formula correctly recovers volatility function from European call option price in hyperbolic-sine model. © Springer Nature Switzerland AG 2020.

Authors

Publisher

Springer Verlag

Language

English

Pages

3-10

Status

Published

Volume

1140 CCIS

Year

2020

Organizations

^{1}Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation

Keywords

Dupire formula; Hyperbolic-sine process; Stochastic models; Volatility function

Date of creation

02.11.2020

Date of change

02.11.2020

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Proceedings of 2019 the 9th International Workshop on Computer Science and Engineering, WCSE 2019.
International Workshop on Computer Science and Engineering (WCSE).
2020.
P. 847-852

Article

Lecture Notes in Networks and Systems.
Springer.
Vol. 115.
2020.
P. 59-66