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.

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

scholarly journals On a New Corporate Bond Pricing Model with Potential Credit Rating Change and Stochastic Interest Rate

2018 ◽  
Vol 11 (4) ◽  
pp. 87 ◽  
Author(s):  
Hong-Ming Yin ◽  
Jin Liang ◽  
Yuan Wu
Keyword(s):  
Interest Rate ◽  
Credit Rating ◽  
Corporate Bond ◽  
Bond Pricing ◽  
Stochastic Interest Rate ◽  
Pricing Model ◽  
New Model ◽  
Stochastic Interest ◽  
The Interest Rate ◽  
Rating Change

In this paper, we consider a new corporate bond-pricing model with credit-rating migration risks and a stochastic interest rate. In the new model, the criterion for rating change is based on a predetermined ratio of the corporation’s total asset and debt. Moreover, the rating changes are allowed to happen a finite number of times during the life-span of the bond. The volatility of a corporate bond price may have a jump when a credit rating for the bond is changed. Moreover, the volatility of the bond is also assumed to depend on the interest rate. This new model improves the previous existing bond models in which the rating change is only allowed to occur once with an interest-dependent volatility or multi-ratings with constant interest rate. By using a Feynman-Kac formula, we obtain a free boundary problem. Global existence and uniqueness are established when the interest rate follows a Vasicek’s stochastic process. Calibration of the model parameters and some numerical calculations are shown.

scholarly journals Lookback Option Pricing Problems of Uncertain Mean-Reverting Stock Model

2021 ◽  
Vol 25 (5) ◽  
pp. 539-545
Author(s):  
Zhaopeng Liu ◽  
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Asset Price ◽  
Option Price ◽  
Cir Model ◽  
Lookback Option ◽  
Proposed Model ◽  
Stock Model ◽  
Path Dependent ◽  
The Interest Rate

A lookback option is a path-dependent option, offering a payoff that depends on the maximum or minimum value of the underlying asset price over the life of the option. This paper presents a new mean-reverting uncertain stock model with a floating interest rate to study the lookback option price, in which the processing of the interest rate is assumed to be the uncertain counterpart of the Cox–Ingersoll–Ross (CIR) model. The CIR model can reflect the fluctuations in the interest rate and ensure that such rate is positive. Subsequently, lookback option pricing formulas are derived through the α-path method and some mathematical properties of the uncertain option pricing formulas are discussed. In addition, several numerical examples are given to illustrate the effectiveness of the proposed model.

Defined contribution pension planning with a stochastic interest rate and mean-reverting returns under the hyperbolic absolute risk aversion preference

2019 ◽  
Author(s):  
Hao Chang ◽  
Chunfeng Wang ◽  
Zhenming Fang ◽  
Dan Ma
Keyword(s):  
Interest Rate ◽  
Absolute Risk ◽  
Market Price ◽  
Optimal Strategies ◽  
Stochastic Interest Rate ◽  
Market Price Of Risk ◽  
Absolute Risk Aversion ◽  
Stochastic Interest ◽  
Price Of Risk ◽  
The Interest Rate

Abstract The interest rate and the market price of risk may be stochastic in a real-world financial market. In this paper, the interest rate is assumed to be driven by a stochastic affine interest rate model and the market price of risk from the stock market is a mean-reverting process. In addition, the dynamics of the stock are simultaneously driven by random sources of interest rate and the stock market itself. In pension fund management, different fund managers may have different risk preferences. We suppose risk preference is described by the hyperbolic absolute risk aversion utility, which is a general utility function describing different risk preferences. Legendre transform-dual theory is presented to successfully obtain explicit expressions for optimal strategies. A numerical example illustrates the sensitivity of optimal strategies to market parameters. Theoretical results imply that the risks from stochastic interest rate and stochastic return may be completely hedged by adopting specific portfolios.

scholarly journals Bond portfolio's duration and investment term-structure management problem

2006 ◽  
Vol 2006 ◽  
pp. 1-19
Author(s):  
Daobai Liu
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Interest Rate Risk ◽  
Management Problem ◽  
Short Term ◽  
Bond Portfolio ◽  
Stochastic Interest ◽  
Bond Portfolios ◽  
Interest Rate Model ◽  
The Interest Rate

In the considered bond market, there are N zero-coupon bonds transacted continuously, which will mature at equally spaced dates. A duration of bond portfolios under stochastic interest rate model is introduced, which provides a measurement for the interest rate risk. Then we consider an optimal bond investment term-structure management problem using this duration as a performance index, and with the short-term interest rate process satisfying some stochastic differential equation. Under some technique conditions, an optimal bond portfolio process is obtained.

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