Market calibration under a long memory stochastic volatility model. (English) Zbl 1396.91760

Pospíšil, Jan; Sobotka, Tomáš

Appl. Math. Finance 23, No. 5-6, 323-343 (2016).

Summary: In this article, we study a long memory stochastic volatility model (LSV), under which stock prices follow a jump-diffusion stochastic process and its stochastic volatility is driven by a continuous-time fractional process that attains a long memory. LSV model should take into account most of the observed market aspects and unlike many other approaches, the volatility clustering phenomenon is captured explicitly by the long memory parameter. Moreover, this property has been reported in realized volatility time-series across different asset classes and time periods. In the first part of the article, we derive an alternative formula for pricing European securities. The formula enables us to effectively price European options and to calibrate the model to a given option market. In the second part of the article, we provide an empirical review of the model calibration. For this purpose, a set of traded FTSE 100 index call options is used and the long memory volatility model is compared to a popular pricing approach – the Heston model. To test stability of calibrated parameters and to verify calibration results from previous data set, we utilize multiple data sets from NYSE option market on Apple Inc. stock.

MSC:

91G20	Derivative securities (option pricing, hedging, etc.)
60G22	Fractional processes, including fractional Brownian motion
60J75	Jump processes (MSC2010)

Keywords:

European call option; stochastic volatility; long memory; fractional process; market calibration

Software:

Mathematica; longmemo

References:

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