Asset Pricing with Stochastic Volatility

Gopinath Kallianpur and Rajeeva L. Karandikar
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Gopinath Kallianpur: University of North Carolina, Department of Statistics
Rajeeva L. Karandikar: Indian Statistical Institute, Department of Mathematics & Statistics

Chapter 13 in Introduction to Option Pricing Theory, 2000, pp 225-239 from Springer

Abstract: Abstract We consider a market consisting of a stock St and a bond Bt governed by the following equations: 13.1 $$d{S_t} = a(t,{S_t}){S_t}dt + {\sigma _t}{S_t}d{W_t} $$ and 13.2 $${\text{d}}{{\text{B}}_{\text{t}}}{\text{ = }}{{\text{r}}_{\text{t}}}{{\text{B}}_{\text{t}}}{\text{dt,}} {{\text{B}}_{\text{0}}}{\text{ = 1}}$$ where Wt is a Brownian motion, S0 is a given random variable independent of W, rt is a bounded, non-negative, progressively measurable interest rate process.

Keywords: Brownian Motion; Markov Process; Stock Price; Asset Price; Stochastic Differential Equation (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0511-1_13

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DOI: 10.1007/978-1-4612-0511-1_13

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