Barrier Option Pricing in the Sub-Mixed Fractional Brownian Motion with Jump Environment

Abstract

This paper investigates the pricing formula for barrier options where the underlying asset is driven by the sub-mixed fractional Brownian motion with jump. By applying the corresponding Ito^’s formula, the B-S type PDE is derived by a self-financing strategy. Furthermore, the explicit pricing formula for barrier options is obtained through converting the PDE to the Cauchy problem. Numerical experiments are conducted to test the impact of the barrier price, the Hurst index, the jump intensity and the volatility on the value of barrier option respectively.

Pricing European Options under a Fuzzy Mixed Weighted Fractional Brownian Motion Model with Jumps

“…Bian and Li [22] used stochastic analysis, fractal theory, and fuzzy set theory to construct a European option pricing model based on the long-term memory property of the financial market in an uncertain environment, and the conclusions showed that the European option pricing model with long-term memory property was more suitable for financial markets in an uncertain environment. More related studies can be referred to in [23][24][25]. To tackle these challenges, we propose a new framework for pricing European options under a fuzzy mixed weighted-fBm model with jumps.…”

Pricing Strategy of Convertible Bond with Memory and Jumps

“…In [14] Marina etc, derived the explicit formula for Asian options, where the underlying asset is driven by jumpdiffusion. Ji et al [13] investigated the pricing of barrier option when the underlying asset is driven by a Sub-mixed fractional Brownian motion.…”