Glossary

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Heston model

The Heston model (Heston, 1993) is a generalisation of the standard Black-Scholes model to incorporate stochastic volatility. The Heston model satisfies the following system of SDE:s
dS(t)=μS(t)dt+(V(t))1/2dW1(t), S(0)=s0,
dV(t)=κ(θ-V(t))dt+σ(V(t))1/2dW2(t),V(0)=v0,
where μ>0,κ>0,θ>0,σ>0. Usually one also wants to have κθ>σ2/2 (Feller, 1951) to guarantee that V stays strictly positive.

References

Heston, Steven L. (1993). A Closed-Form Solution for Options with Stochastic Volatility with Application to Bond and Currency Options, The Review of Financial Studies 6, 327-343. Journal article.
Feller, W. (1951): Two Singular Diffusion Problems, Annals of Mathematics, 54 , 173-182. Journal article

 

Questions: Magnus Wiktorsson
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