A note on “A closed-form pricing formula for European options under the Heston model with stochastic interest rate”

2019 ◽  
Vol 350 ◽  
pp. 55-56
Author(s):  
Xinfeng Ruan ◽  
Wenjun Zhang
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Heston Model ◽  
Stochastic Interest Rate ◽  
European Options ◽  
Stochastic Interest ◽  
Pricing Formula

A semi-analytical pricing formula for European options under the rough Heston-CIR model

2020 ◽  
Vol 61 ◽  
pp. 431-445
Author(s):  
Xin-Jiang He ◽  
Sha Lin
Keyword(s):  
Interest Rate ◽  
Heston Model ◽  
European Options ◽  
Cir Model ◽  
Stochastic Nature ◽  
Special Cases ◽  
Stochastic Interest ◽  
Rough Volatility ◽  
The Interest Rate ◽  
Pricing Formula

We combine the rough Heston model and the CIR (Cox–Ingersoll–Ross) interest rate together to form a rough Heston-CIR model, so that both the rough behaviour of the volatility and the stochastic nature of the interest rate can be captured. Despite the convoluted structure and non-Markovian property of this model, it still admits a semi-analytical pricing formula for European options, the implementation of which involves solving a fractional Riccati equation. The rough Heston-CIR model is more general, taking both the rough Heston model and the Heston-CIR model as special cases. The influence of rough volatility and stochastic interest rate is shown to be significant through numerical experiments. doi:10.1017/S1446181120000024

A SEMI-ANALYTICAL PRICING FORMULA FOR EUROPEAN OPTIONS UNDER THE ROUGH HESTON-CIR MODEL

2019 ◽  
Vol 61 (4) ◽  
pp. 431-445
Author(s):  
XIN-JIANG HE ◽  
SHA LIN
Keyword(s):  
Interest Rate ◽  
Heston Model ◽  
European Options ◽  
Cir Model ◽  
Stochastic Nature ◽  
Special Cases ◽  
Stochastic Interest ◽  
Rough Volatility ◽  
The Interest Rate ◽  
Pricing Formula

We combine the rough Heston model and the CIR (Cox–Ingersoll–Ross) interest rate together to form a rough Heston-CIR model, so that both the rough behaviour of the volatility and the stochastic nature of the interest rate can be captured. Despite the convoluted structure and non-Markovian property of this model, it still admits a semi-analytical pricing formula for European options, the implementation of which involves solving a fractional Riccati equation. The rough Heston-CIR model is more general, taking both the rough Heston model and the Heston-CIR model as special cases. The influence of rough volatility and stochastic interest rate is shown to be significant through numerical experiments.

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.

PRICING OPTIONS UNDER STOCHASTIC INTEREST RATE AND THE FRASCA–FARINA PROCESS: A SIMPLE, EXPLICIT FORMULA

2021 ◽  
pp. 2150003
Author(s):  
MOAWIA ALGHALITH
Keyword(s):  
Interest Rate ◽  
Simple Formula ◽  
Stochastic Interest Rate ◽  
European Options ◽  
Pricing Options ◽  
Black Scholes Model ◽  
Stochastic Interest ◽  
Black Scholes ◽  
Practical Complexity ◽  
Theoretical Limitation

Assuming a stochastic interest rate, we introduce a simple formula for pricing European options. In doing so, we provide a complete closed-form formula that does not require any numerical/computational methods. Furthermore, the model and formula are far simpler than the previous models/formulas. Our formula is as simple as the classical Black–Scholes pricing formula. Moreover, it removes the theoretical limitation of the original Black–Scholes model without any added practical complexity.

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