On the valuation of variance swaps with stochastic volatility

2012 ◽  
Vol 219 (4) ◽  
pp. 1654-1669 ◽  
Author(s):  
Song-Ping Zhu ◽  
Guang-Hua Lian
Keyword(s):  
Stochastic Volatility ◽  
Variance Swaps

PRICING VARIANCE SWAPS UNDER DOUBLE HESTON STOCHASTIC VOLATILITY MODEL WITH STOCHASTIC INTEREST RATE

2021 ◽  
pp. 1-17
Author(s):  
Huojun Wu ◽  
Zhaoli Jia ◽  
Shuquan Yang ◽  
Ce Liu
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Characteristic Functions ◽  
Stochastic Interest Rate ◽  
Modeling Framework ◽  
Variance Swaps ◽  
Volatility Model ◽  
Stochastic Interest

In this paper, we discuss the problem of pricing discretely sampled variance swaps under a hybrid stochastic model. Our modeling framework is a combination with a double Heston stochastic volatility model and a Cox–Ingersoll–Ross stochastic interest rate process. Due to the application of the T-forward measure with the stochastic interest process, we can only obtain an efficient semi-closed form of pricing formula for variance swaps instead of a closed-form solution based on the derivation of characteristic functions. The practicality of this hybrid model is demonstrated by numerical simulations.

A NOVEL ANALYTICAL APPROACH FOR PRICING DISCRETELY SAMPLED GAMMA SWAPS IN THE HESTON MODEL

2016 ◽  
Vol 57 (3) ◽  
pp. 244-268
Author(s):  
SANAE RUJIVAN
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Analytical Approach ◽  
Solution Procedure ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Variance Swaps ◽  
Closed Form Solutions ◽  
Volatility Model ◽  
Closed Form Formula

The main purpose of this paper is to present a novel analytical approach for pricing discretely sampled gamma swaps, defined in terms of weighted variance swaps of the underlying asset, based on Heston’s two-factor stochastic volatility model. The closed-form formula obtained in this paper is in a much simpler form than those proposed in the literature, which substantially reduces the computational burden and can be implemented efficiently. The solution procedure presented in this paper can be adopted to derive closed-form solutions for pricing various types of weighted variance swaps, such as self-quantoed variance and entropy swaps. Most interestingly, we discuss the validity of the current solutions in the parameter space, and provide market practitioners with some remarks for trading these types of weighted variance swaps.

scholarly journals Apreçamento de Ativos Referenciados em Volatilidade

2006 ◽  
Vol 4 (2) ◽  
pp. 203
Author(s):  
Alan De Genaro Dario
Keyword(s):  
Stochastic Volatility ◽  
Foreign Currency ◽  
Asset Price ◽  
Realized Volatility ◽  
Contingent Claims ◽  
Stochastic Volatility Model ◽  
Currency Options ◽  
Variance Swaps ◽  
Volatility Model ◽  
Future Realized Volatility

Volatility swaps are contingent claims on future realized volatility. Variance swaps are similar instruments on future realized variance, the square of future realized volatility. Unlike a plain vanilla option, whose volatility exposure is contaminated by its asset price dependence, volatility and variance swaps provide a pure exposure to volatility alone. This article discusses the risk-neutral valuation of volatility and variance swaps based on the framework outlined in the Heston (1993) stochastic volatility model. Additionally, the Heston (1993) model is calibrated for foreign currency options traded at BMF and its parameters are used to price swaps on volatility and variance of the BRL / USD exchange rate.

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