Swap Rate à la Stock: Bermudan Swaptions Made Easy

Wilmott ◽  
2020 ◽  
Vol 2020 (109) ◽  
pp. 44-51
Author(s):  
Dariusz Gatarek ◽  
Juliusz Jabłecki
Keyword(s):  
Bermudan Swaptions

scholarly journals Fast and accurate exercise policies for Bermudan swaptions in the LIBOR market model

2016 ◽  
Vol 03 (01) ◽  
pp. 1650005 ◽  
Author(s):  
Patrik Karlsson ◽  
Shashi Jain ◽  
Cornelis W. Oosterlee
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Simulations ◽  
Upper Bound ◽  
Market Model ◽  
Monte Carlo Approach ◽  
Lower Upper ◽  
Libor Market Model ◽  
Bermudan Swaptions

This paper describes an American Monte Carlo approach for obtaining fast and accurate exercise policies for pricing of callable LIBOR Exotics (e.g., Bermudan swaptions) in the LIBOR market model using the Stochastic Grid Bundling Method (SGBM). SGBM is a bundling and regression based Monte Carlo method where the continuation value is projected onto a space where the distribution is known. We also demonstrate an algorithm to obtain accurate and tight lower–upper bound values without the need for nested Monte Carlo simulations.

scholarly journals Between Scylla and Charybdis: The Bermudan Swaptions Pricing Odyssey

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 112
Author(s):  
Dariusz Gatarek ◽  
Juliusz Jabłecki
Keyword(s):  
Interest Rate ◽  
One Dimensional ◽  
Classic Result ◽  
Implementation Techniques ◽  
Interest Rate Swaps ◽  
Exercise Boundary ◽  
Bermudan Swaptions ◽  
Main Ideas ◽  
Multidimensional Process ◽  
Theoretical Side

Bermudan swaptions are options on interest rate swaps which can be exercised on one or more dates before the final maturity of the swap. Because the exercise boundary between the continuation area and stopping area is inherently complex and multi-dimensional for interest rate products, there is an inherent “tug of war” between the pursuit of calibration and pricing precision, tractability, and implementation efficiency. After reviewing the main ideas and implementation techniques underlying both single- and multi-factor models, we offer our own approach based on dimension reduction via Markovian projection. Specifically, on the theoretical side, we provide a reinterpretation and extension of the classic result due to Gyöngy which covers non-probabilistic, discounted, distributions relevant in option pricing. Thus, we show that for purposes of swaption pricing, a potentially complex and multidimensional process for the underlying swap rate can be collapsed to a one-dimensional one. The empirical contribution of the paper consists in demonstrating that even though we only match the marginal distributions of the two processes, Bermudan swaptions prices calculated using such an approach appear well-behaved and closely aligned to counterparts from more sophisticated models.

MARKOV MARKET MODEL CONSISTENT WITH CAP SMILE

2000 ◽  
Vol 03 (02) ◽  
pp. 161-181 ◽  
Author(s):  
P. BALLAND ◽  
L. P. HUGHSTON
Keyword(s):  
Normal Distribution ◽  
Implied Volatility ◽  
Market Model ◽  
Interest Rate Models ◽  
Market Models ◽  
Forward Measure ◽  
Black Scholes ◽  
Log Normal ◽  
Bermudan Swaptions ◽  
Log Normal Distribution

New interest rate models have emerged recently in which distributional assumptions are made directly on financial observables. In these "Market Models" the Libor rates have a log-normal distribution in the corresponding forward measure, and caps are priced according to the Black–Scholes formula. These models present two disadvantages. First, Libor rates do not in reality have a log-normal distribution since the implied volatility of a cap depends typically on the strike. Second, these models are difficult to use for pricing derivatives other than caps. In this paper, we extend these models to allow for a broader class of Libor rate distributions. In particular, we construct multi-factor Market Models that are consistent with an initial cap smile surface, and have the useful feature of exhibiting Markovian Libor rates. We show that these Markov Market Models can be used relatively easily to price complex Libor derivatives, such as Bermudan swaptions, captions or flexi-caps, by construction of a tree of Libor rates.

LEAST SQUARES MONTE CARLO CREDIT VALUE ADJUSTMENT WITH SMALL AND UNIDIRECTIONAL BIAS

2016 ◽  
Vol 19 (08) ◽  
pp. 1650048 ◽  
Author(s):  
MARK JOSHI ◽  
OH KANG KWON
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Global Financial Crisis ◽  
Regression Function ◽  
Cash Flows ◽  
Least Squares Monte Carlo ◽  
Early Exercise ◽  
Regression Functions ◽  
The Global Financial Crisis ◽  
Bermudan Swaptions

Credit value adjustment (CVA) and related charges have emerged as important risk factors following the Global Financial Crisis. These charges depend on uncertain future values of underlying products, and are usually computed by Monte Carlo simulation. For products that cannot be valued analytically at each simulation step, the standard market practice is to use the regression functions from least squares Monte Carlo method to approximate their values. However, these functions do not necessarily provide accurate approximations to product values over all simulated paths and can result in biases that are difficult to control. Motivated by a novel characterization of the CVA as the value of an option with an early exercise opportunity at a stochastic time, we provide an approximation for CVA and other credit charges that rely only on the sign of the regression functions. The values are determined, instead, by pathwise deflated cash flows. A comparison of CVA for Bermudan swaptions and cancellable swaps shows that the proposed approximation results in much smaller errors than the standard approach of using the regression function values.

IMPLICATIONS FOR HEDGING OF THE CHOICE OF DRIVING PROCESS FOR ONE-FACTOR MARKOV-FUNCTIONAL MODELS

2013 ◽  
Vol 16 (05) ◽  
pp. 1350030
Author(s):  
JOANNE E. KENNEDY ◽  
DUY PHAM
Keyword(s):  
Markov Process ◽  
Strong Evidence ◽  
Functional Model ◽  
One Dimensional ◽  
Functional Models ◽  
Hedging Portfolio ◽  
The One ◽  
Bermudan Swaptions ◽  
Delta Hedge ◽  
Instantaneous Volatility

In this paper, we study the implications for hedging Bermudan swaptions of the choice of the instantaneous volatility for the driving Markov process of the one-dimensional swap Markov-functional model. We find that there is a strong evidence in favor of what we term "parametrization by time" as opposed to "parametrization by expiry". We further propose a new parametrization by time for the driving process which takes as inputs into the model the market correlations of relevant swap rates. We show that the new driving process enables a very effective vega-delta hedge with a much more stable gamma profile for the hedging portfolio compared with the existing ones.

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