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Asset Pricing with Stochastic Volatility

In: Introduction to Option Pricing Theory

Author

Listed:
  • Gopinath Kallianpur

    (University of North Carolina, Department of Statistics)

  • Rajeeva L. Karandikar

    (Indian Statistical Institute, Department of Mathematics & Statistics)

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.

Suggested Citation

  • Gopinath Kallianpur & Rajeeva L. Karandikar, 2000. "Asset Pricing with Stochastic Volatility," Springer Books, in: Introduction to Option Pricing Theory, chapter 13, pages 225-239, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0511-1_13
    DOI: 10.1007/978-1-4612-0511-1_13
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