Pricing Option on Jump Diffusion and Stochastic Interest Rates Model

2011 ◽  
Vol 50-51 ◽  
pp. 723-727
Author(s):  
Bo Peng ◽  
Zhi Hui Wu
Keyword(s):  
Interest Rates ◽  
Stock Price ◽  
Special Kind ◽  
Jump Process ◽  
Jump Diffusion ◽  
Time Interval ◽  
Martingale Method ◽  
Stochastic Interest Rates ◽  
Stochastic Interest ◽  
Jump Diffusion Model

This paper assumed that the stock price jump process for a special kind of renewal jump process, that is incident time interval for independent and subordinate to Gamma distribution random variable sequence. We obtain the European bi-direction option pricing formulas on jump diffusion model under the stochastic interest rates by simply mathematical induce by means of martingale method.

Pricing of Some Exotic Options under Jump Diffusion and Stochastic Interest Rates Model

2011 ◽  
Vol 109 ◽  
pp. 405-409
Author(s):  
Bo Peng
Keyword(s):  
Interest Rates ◽  
Poisson Process ◽  
Stock Price ◽  
Jump Process ◽  
Jump Diffusion ◽  
Martingale Method ◽  
Exotic Options ◽  
Stochastic Interest Rates ◽  
Stochastic Interest ◽  
Risk Neutral

This paper assumes that jump process in underlying assets-stock price is more common than Poisson process and derive the pricing formulas of some exotic options under the stochastic interest rates by martingale method with the risk-neutral hypothesis.

scholarly journals The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Chao Wang ◽  
Shengwu Zhou ◽  
Jingyuan Yang
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Jump Diffusion ◽  
Default Intensity ◽  
Stochastic Interest ◽  
Jump Diffusion Model ◽  
Vulnerable Option ◽  
Vulnerable Options

Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. With the changes of measures, the traditional pricing method is simplified and the general pricing formula is obtained for the European vulnerable option with stochastic interest rate. At the same time, the explicit expression for it comes into being.

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