American Options in the Heston Model with Stochastic Interest Rate and Its Generalizations

2013 ◽  
Vol 20 (1) ◽  
pp. 26-49 ◽  
Author(s):  
Svetlana Boyarchenko ◽  
Sergei LevendorskiĬ
Keyword(s):  
Interest Rate ◽  
American Options ◽  
Heston Model ◽  
Stochastic Interest Rate ◽  
Stochastic Interest

EQUILIBRIUM PRICE OF VARIANCE SWAPS UNDER STOCHASTIC VOLATILITY WITH LÉVY JUMPS AND STOCHASTIC INTEREST RATE

2019 ◽  
Vol 22 (04) ◽  
pp. 1950016 ◽  
Author(s):  
BEN-ZHANG YANG ◽  
JIA YUE ◽  
NAN-JING HUANG
Keyword(s):  
Interest Rate ◽  
Stock Price ◽  
Moment Generating Function ◽  
Heston Model ◽  
Martingale Measure ◽  
Stochastic Interest Rate ◽  
Variance Swaps ◽  
Jump Risks ◽  
Stochastic Interest ◽  
Lévy Jumps

This paper focuses on the pricing of variance swaps in incomplete markets where the short rate of interest is determined by a Cox–Ingersoll–Ross model and the stock price is determined by a Heston model with simultaneous Lévy jumps. We obtain the pricing kernel and the equivalent martingale measure in an equilibrium framework. We also give new closed-form solutions for the delivery prices of discretely sampled variance swaps under the forward measure, as opposed to the risk neural measure, by employing the joint moment generating function of underlying processes. Theoretical results and numerical examples are provided to illustrate how the values of variance swaps depend on the jump risks and stochastic interest rate.

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