Stochastic Volatility for Interest Rate Derivatives

Kaisajuntti, Linus; Kennedy, J. E.

doi:10.2139/ssrn.1894887

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…Despite the fact that single-factor models (see, for instance, Vasicek 1977, Cox et al 1985 are appealing for their easy tractability, the assumption of a term structure driven by more than one state variable (see, for instance, Brennan & Schwartz 1979, Schaefer & Schwartz 1984, Longstaff & Schwartz 1992, Fong & Vasicek 1991 is more appropriate to describe the stylized facts of interest rates and to obtain consistent valuations of interest-sensitive claims. This aspect has been recently confirmed by Kaisajuntti & Kennedy (2014), who investigate the influence of introducing a stochastic volatility driver process when computing the price of interest-sensitive claims. Describing accurately interest rate volatility is also crucial for several aspects as valuing fixed-income securities and managing fixed-income portfolios.…”

Section: Introductionmentioning

confidence: 75%

A Lattice-Based Model for Evaluating Bonds and Interest-Sensitive Claims Under Stochastic Volatility

Russo

Staino

2018

Int. J. Theor. Appl. Finan.

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We propose a flexible lattice model for pricing bonds and interest-sensitive claims under stochastic volatility, which is able to accommodate different dynamics specifications, and permits correlation between the interest rate and volatility diffusion. The model is based on the forward shooting grid method where the volatility process, as the primary state variable, is discretized by means of a recombining binomial tree. Then, the interest rate, as the auxiliary state variable, is discretized by attaching a subset of representative realizations to each node of the volatility lattice to cover the range of possible interest rates at each time slice. Finally, we develop a bivariate lattice presenting four branches for each node, where the joint probabilities for the possible jumps embed the correlation. Since the model works on representative interest rate values, a linear interpolation technique is used when solving backward through the lattice to compute the bond present value or the interest-sensitive claim price.

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Section: Introductionmentioning

confidence: 75%

A Lattice-Based Model for Evaluating Bonds and Interest-Sensitive Claims Under Stochastic Volatility

Russo

Staino

2018

Int. J. Theor. Appl. Finan.

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show abstract

“…We consider the following data: T = 12 months, D = 4, d i = i×T D , F l = −0.02, C l = 0.02, F g = 0, C g = 0.2 and the payoff (19). We price the cliquet option with DSabr I and DSabr II models, in single precision.…”

Section: Pricing a Cliquet Optionmentioning

confidence: 99%

“…In [20] a second order approximation to call options prices and implied volatilities is proposed and a closed form approximation of the option price extending dynamically the original SABR model is gained. In [19] the SABR model with a time-dependent volatility function and a mean reverting volatility process is obtained. In [4] a hybrid SABR−Hull-White model for long-maturity equity derivatives is considered.…”

Section: Introductionmentioning

confidence: 99%