Stochastic volatility for interest rate derivatives

Kaisajuntti, Linus; Kennedy, J. E.

doi:10.1080/14697688.2012.757848

Cited by 2 publications

(7 citation statements)

References 7 publications

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“…For example, Fouque, Papanicolaou, and Sircar (2000), Masoliver and Perello (2006) and Perello, Sircar, and Masoliver (2008) studied the equity market and investigated why the mean reverting behaviour of the volatility process is needed to explain the data (S&P 500 and Dow Jones Industrial Average indices). In case of the interest rate market, the works by Kaisajuntti and Kennedy (2014), Piterbarg (2005) and the most recent paper by Antonov and Spector (2012) also agree that the mean reverting volatility set-up is needed especially for large time horizons. A particular form of the SABR-MR model was studied in Kaisajuntti and Kennedy (2014) within the context of swaption data.…”

Section: Introductionmentioning

confidence: 81%

“…In case of the interest rate market, the works by Kaisajuntti and Kennedy (2014), Piterbarg (2005) and the most recent paper by Antonov and Spector (2012) also agree that the mean reverting volatility set-up is needed especially for large time horizons. A particular form of the SABR-MR model was studied in Kaisajuntti and Kennedy (2014) within the context of swaption data. The authors found that mean reversion will be essential if one wishes to provide a low-dimensional model for the level of rates.…”

Section: Introductionmentioning

confidence: 81%

“…We now look at our main model of interest, the SABR with mean reversion model which will be referred to as the SABR-MR model. The form of the SABR-MR model we choose to study is as in Kaisajuntti and Kennedy (2014) …”

Section: The Sabr and Sabr With Mean Reversion Models (Sabr-mr)mentioning

confidence: 99%

“…In fact, this is a special case of the more well-known and general function gðÁÞ ¼ ½a þ bðT À tÞ expfcðT À tÞg þ d as proposed in Rebonato (2002), Rebonato (2007) and Rebonato et al (2009). For the reasons for this particular choice of function, we refer to the earlier paper by Kaisajuntti and Kennedy (2014). Note that U is an OU process with κ being the mean reversion parameter.…”

Section: The Sabr and Sabr With Mean Reversion Models (Sabr-mr)mentioning

confidence: 99%

“…In the interest rate context, this specific form of model was first introduced in Kaisajuntti and Kennedy (2014) with the original motivation coming from a numerical investigation of 10-year tenor swap rates of different start dates (2-30 years) to model the level of rates. As discussed in Kaisajuntti and Kennedy (2014), ν has the role of controlling the overall curvature of different smiles across expiries while κ controls the dampening over time.…”

Section: The Sabr and Sabr With Mean Reversion Models (Sabr-mr)mentioning

confidence: 99%

See 4 more Smart Citations

On the Approximation of the SABR with Mean Reversion Model: A Probabilistic Approach

Kennedy

Pham

2014

Applied Mathematical Finance

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In this paper, we study the stochastic alpha beta rho with mean reversion model (SABR-MR). We first compare the SABR model with the SABR-MR model in terms of future volatility to point out the fundamental difference in the models' dynamics. We then derive an efficient probabilistic approximation for the SABR-MR model to price European options. Similar to the method derived in Kennedy, J. E., Mitra, S., & Pham, D. (2012). On the approximation of the SABR model: A probabilistic approach. Applied Mathematical Finance, 19(6), 553-586., we focus on capturing the terminal distribution of the underlying asset (conditional on the terminal volatility) to arrive at the implied volatilities of the corresponding European options for all strikes and maturities. Our resulting method allows us to work with a wide range of parameters that cover the long-dated option and different market conditions.

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Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 81%

Section: The Sabr and Sabr With Mean Reversion Models (Sabr-mr)mentioning

confidence: 99%

Section: The Sabr and Sabr With Mean Reversion Models (Sabr-mr)mentioning

confidence: 99%

Section: The Sabr and Sabr With Mean Reversion Models (Sabr-mr)mentioning

confidence: 99%

See 3 more Smart Citations

On the Approximation of the SABR with Mean Reversion Model: A Probabilistic Approach

Kennedy

Pham

2014

Applied Mathematical Finance

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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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Stochastic volatility for interest rate derivatives

Cited by 2 publications

References 7 publications

On the Approximation of the SABR with Mean Reversion Model: A Probabilistic Approach

On the Approximation of the SABR with Mean Reversion Model: A Probabilistic Approach

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

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