Interest Rate Volatility and No-Arbitrage Affine Term Structure Models

2013 ◽  
Author(s):  
Scott Joslin ◽  
Anh Le
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Affine Term Structure ◽  
No Arbitrage ◽  
Affine Term Structure Models ◽  
Term Structure Models ◽  
Interest Rate Volatility

Interest Rate Volatility and No-Arbitrage Affine Term Structure Models

2021 ◽  
Author(s):  
Scott Joslin ◽  
Anh Le
Keyword(s):  
Term Structure ◽  
Affine Term Structure ◽  
No Arbitrage ◽  
Affine Term Structure Models ◽  
Term Structure Models ◽  
Second Moments ◽  
Interest Rate Volatility ◽  
Rich Information ◽  
The Rich ◽  
Absence Of Arbitrage

Within the affine framework, many have observed a tension between matching conditional first and second moments in dynamic term structure models (DTSMs). Although the existence of this tension is generally accepted, less understood is the mechanism that underlies it. We show that no arbitrage along with the rich information in the cross section of yields has strong implications for both the dynamics of volatility and the forecasts of yields. We show that this link implied by the absence of arbitrage—and not the factor structure per se—underlies the tension between first and second moments found in the literature. Adding to recent research that has suggested that no-arbitrage restrictions are nearly irrelevant in Gaussian DTSMs, our results show that no-arbitrage restrictions are potentially relevant when there is stochastic volatility. This paper was accepted by Gustavo Manso, finance.

Pricing interest rate derivatives under stochastic volatility

2011 ◽  
Vol 37 (1) ◽  
pp. 72-91 ◽  
Author(s):  
Nabil Tahani ◽  
Xiaofei Li
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Term Structure ◽  
Alternative Methods ◽  
Future Research ◽  
Content Type ◽  
Interest Rate Derivatives ◽  
Affine Term Structure ◽  
Affine Term Structure Models ◽  
Term Structure Models

PurposeThe purpose of this paper is to derive semi‐closed‐form solutions to a wide variety of interest rate derivatives prices under stochastic volatility in affine‐term structure models.Design/methodology/approachThe paper first derives the Frobenius series solution to the cross‐moment generating function, and then inverts the related characteristic function using the Gauss‐Laguerre quadrature rule for the corresponding cumulative probabilities.FindingsThis paper values options on discount bonds, coupon bond options, swaptions, interest rate caps, floors, and collars, etc. The valuation approach suggested in this paper is found to be both accurate and fast and the approach compares favorably with some alternative methods in the literature.Research limitations/implicationsFuture research could extend the approach adopted in this paper to some non‐affine‐term structure models such as quadratic models.Practical implicationsThe valuation approach in this study can be used to price mortgage‐backed securities, asset‐backed securities and credit default swaps. The approach can also be used to value derivatives on other assets such as commodities. Finally, the approach in this paper is useful for the risk management of fixed‐income portfolios.Originality/valueThis paper utilizes a new approach to value many of the most commonly traded interest rate derivatives in a stochastic volatility framework.

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