Chapman–Kolmogorov lattice method for derivatives pricing

Aluigi, Federico; Corradini, Massimiliano; Gheno, Andrea

doi:10.1016/j.amc.2013.11.001

Cited by 4 publications

(6 citation statements)

References 23 publications

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“…By solving system (24) (for each date, bank and maturity), we obtain , and ( 1,3,5,7,10). The model asset volatility term structures are reported in Table 4 and the barrier levels obtained by calibration are shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Recovering survival probabilities 1499 where is the risk-free stochastic discount factor from T to t, is the first date after , is the fraction of a year between and . Independently from the model chosen for the default time , the CDS can be priced by riskneutral valuation 1 :…”

Section: Credit Default Swapsmentioning

confidence: 99%

“…Step Step 3. Survival probabilities computation Survival probabilities for times ( 1,3,5,7,10), are obtained numerically from Eqs. (18) and (19).…”

Section: Model Implementationmentioning

confidence: 99%

See 2 more Smart Citations

Recovering survival probabilities from equity option prices and credit default swap spreads

Aluigi¹,

Gheno²

2018

ams

Self Cite

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After the financial crisis onset in 2007, the interest in credit risk assessment has grown exponentially and there is an even more pressing need for efficient credit risk models. To this aim we introduce a credit risk structural model that is consistent with both the equity option and the credit default swap markets. It provides survival probabilities that can be used for market consistent pricing of over-the-counter structured products. Empirical evidence of the model accuracy and efficiency is given by using Goldman Sachs, J.P. Morgan Chase and Morgan Stanley market data prior to, during and after the Lehman Brothers default.

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Section: Resultsmentioning

confidence: 99%

Section: Credit Default Swapsmentioning

confidence: 99%

See 1 more Smart Citation

Recovering survival probabilities from equity option prices and credit default swap spreads

Aluigi¹,

Gheno²

2018

ams

Self Cite

View full text Add to dashboard Cite

show abstract

“…The most widely used methods for calculating this expectation are pde solutions and MC simulations, and a possible alternative is the direct numerical integration of (4), a recent example of this approach can be found in Aluigi et al (2014). Except the American and barrier options, all the other examples described in the last section require accurate interpolation of multiple solutions.…”

Section: The Ghqc Methodsmentioning

confidence: 99%

Fast and simple method for pricing exotic options using Gauss–Hermite quadrature on a cubic spline interpolation

Luo

Shevchenko

2014

J. Finan. Eng.

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There is a vast literature on numerical valuation of exotic options using Monte Carlo (MC), binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it can be convenient and more efficient to utilize direct integration methods to calculate the required option price expectations in a backward time-stepping algorithm. This paper presents a simple, robust and efficient algorithm that can be applied for pricing many exotic options by computing the expectations using Gauss-Hermite integration quadrature applied on a cubic spline interpolation. The algorithm is fully explicit but does not suffer the inherent instability of the explicit finite difference counterpart. A \free" bonus of the algorithm is that it already contains the function for fast and accurate interpolation of multiple solutions required by many discretely monitored path dependent options. For illustrations, we present examples of pricing a series of American options with either Bermudan or continuous exercise features, and a series of exotic path-dependent options of target accumulation redemption note (TARN). Results of the new method are compared with MC and finite difference methods, including some of the most advanced or best known finite difference algorithms in the literature. The comparison shows that, despite its simplicity, the new method can rival with some of the best finite difference algorithms in accuracy and at the same time it is significantly faster. Virtually the same algorithm can be applied to price other path-dependent financial contracts such as Asian options and variable annuities.

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“…The few path-dependent options described in the previous section all require the evaluation of expectation (3). The most widely used methods for calculating this expectation are pde solutions and Monte Carlo simulations, and a possible alternative is the direct numerical integration of (4), a recent example of this approach can be found in Aluigi et al (2014).…”

Section: The Ghqc Methodsmentioning

confidence: 99%

Fast and Simple Method for Pricing Exotic Options Using Gauss-Hermite Quadrature on a Cubic Spline Interpolation

Luo

Shevchenko

2014

SSRN Journal

View full text Add to dashboard Cite

There is a vast literature on numerical valuation of exotic options using Monte Carlo, binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it can be convenient and more efficient to utilize direct integration methods to calculate the required option price expectations in a backward time-stepping algorithm. This paper presents a simple, robust and efficient algorithm that can be applied for pricing many exotic options by computing the expectations using Gauss-Hermite integration quadrature applied on a cubic spline interpolation. The algorithm is fully explicit but does not suffer the inherent instability of the explicit finite difference counterpart. A 'free' bonus of the algorithm is that it already contains the function for fast and accurate interpolation of multiple solutions required by many discretely monitored path dependent options. For illustrations, we present examples of pricing a series of American options with either Bermudan or continuous exercise features, and a series of exotic pathdependent options of target accumulation redemption note (TARN). Results of the new method are compared with Monte Carlo and finite difference methods, including some of the most advanced or best known finite difference algorithms in the literature. The comparison shows that, despite its simplicity, the new method can rival with some of the best finite difference algorithms in accuracy and at the same time it is significantly faster. Virtually the same algorithm can be applied to price other path-dependent financial contracts such as Asian options and variable annuities.

show abstract

Chapman–Kolmogorov lattice method for derivatives pricing

Cited by 4 publications

References 23 publications

Recovering survival probabilities from equity option prices and credit default swap spreads

Recovering survival probabilities from equity option prices and credit default swap spreads

Fast and simple method for pricing exotic options using Gauss–Hermite quadrature on a cubic spline interpolation

Fast and Simple Method for Pricing Exotic Options Using Gauss-Hermite Quadrature on a Cubic Spline Interpolation

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