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Your search keyword '"intensity approach"' showing total 7 results
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7 results on '"intensity approach"'

1. CVA AND VULNERABLE OPTIONS IN STOCHASTIC VOLATILITY MODELS.

Author

ALÒS, E., ANTONELLI, F., RAMPONI, A., and SCARLATTI, S.

Subjects
STOCHASTIC models, MONTE Carlo method, OPTIONS (Finance), MARKET prices, STRUCTURAL models, INTEREST rates
Abstract

This work aims to provide an efficient method to evaluate the Credit Value Adjustment (CVA) for a vulnerable European option, which is an option subject to some default event concerning the issuer solvability. Financial options traded in OTC markets are of this type. In particular, we compute the CVA in some popular stochastic volatility models such as SABR, Hull et al., which have proven to fit quite well market derivatives prices, admitting correlation with the default event. This choice covers the relevant case of Wrong Way Risk (WWR) when a credit deterioration determines an increase in the claim value. Contrary to the structural modeling adopted in [G. Wang, X. Wang & K. Zhu (2017) Pricing vulnerable options with stochastic volatility, Physica A 485, 91–103; C. Ma, S. Yue & Y. Ma (2020) Pricing vulnerable options with Stochastic volatility and Stochastic interest rate, Computational Economics 56, 391–429], we use the reduced-form intensity-based approach to provide an explicit representation formula for the vulnerable option price and related CVA. Later, we specialize the evaluation formula and construct its approximation for the three models mentioned above. Assuming a CIR model for the default intensity process, we run a numerical study to test our approximation, comparing it with Monte Carlo simulations. The results show that for moderate values of the correlation and maturities not exceeding one year, the approximation is very satisfactory as of accuracy and computational time. [ABSTRACT FROM AUTHOR]

Published
2021
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2. CVA in fractional and rough volatility models

Author

Alòs, Elisa, Antonelli, Fabio, Ramponi, Alessandro, and Scarlatti, Sergio

Subjects
Credit Value Adjustment, Vulnerable Options, Rough volatility models, Intensity approach, FOS: Economics and business, Computer Science::Computer Science and Game Theory, Computational Mathematics, Quantitative Finance - Computational Finance, Applied Mathematics, Settore SECS-S/06, Computational Finance (q-fin.CP)
Abstract

In this work we present a general representation formula for the price of a vulnerable European option, and the related CVA in stochastic (either rough or not) volatility models for the underlying's price, when admitting correlation with the default event. We specialize it for some volatility models and we provide price approximations, based on the representation formula. We study numerically their accuracy, comparing the results with Monte Carlo simulations, and we run a theoretical study of the error. We also introduce a seminal study of roughness influence on the claim's price., Comment: 29 pages, 7 figures

Published
2023

4. CVA and Vulnerable Options in Stochastic Volatility Models

Author

Sergio Scarlatti, Elisa Alòs, Alessandro Ramponi, and Fabio Antonelli

Subjects
Computer science, Event (relativity), Monte Carlo method, vulnerable options, Computational Finance (q-fin.CP), SABR volatility model, FOS: Economics and business, Stochastic volatility model, Quantitative Finance - Computational Finance, Credit value adjustment, intensity approach, Econometrics, Economics, Representation (mathematics), Event (probability theory), Actuarial science, Stochastic volatility, Settore SECS-S/06, Work (electrical), Issuer, Pricing of Securities (q-fin.PR), Credit valuation adjustment, General Economics, Econometrics and Finance, Quantitative Finance - Pricing of Securities, Finance
Abstract

This work aims to provide an efficient method to evaluate the Credit Value Adjustment (CVA) for a vulnerable European option, which is an option subject to some default event concerning the issuer solvability. Financial options traded in OTC markets are of this type. In particular, we compute the CVA in some popular stochastic volatility models such as SABR, Hull et al., which have proven to fit quite well market derivatives prices, admitting correlation with the default event. This choice covers the relevant case of Wrong Way Risk (WWR) when a credit deterioration determines an increase in the claim value. Contrary to the structural modeling adopted in [G. Wang, X. Wang & K. Zhu (2017) Pricing vulnerable options with stochastic volatility, Physica A 485, 91–103; C. Ma, S. Yue & Y. Ma (2020) Pricing vulnerable options with Stochastic volatility and Stochastic interest rate, Computational Economics 56, 391–429], we use the reduced-form intensity-based approach to provide an explicit representation formula for the vulnerable option price and related CVA. Later, we specialize the evaluation formula and construct its approximation for the three models mentioned above. Assuming a CIR model for the default intensity process, we run a numerical study to test our approximation, comparing it with Monte Carlo simulations. The results show that for moderate values of the correlation and maturities not exceeding one year, the approximation is very satisfactory as of accuracy and computational time.

Published
2021

5. Intensity-based framework and penalty formulation of optimal stopping problems

Abstract

Financial derivatives commonly contain premature termination clauses, which are embedded rights held by the holder or writer. Well known examples of these stopping rights include the early exercise right in American options, the callable right in callable securities and the prepayment right in mortgage loans. In this paper, we show how to model the mortgagor's prepayment in mortgage loans and the issuer's call in the American warrant as an event risk using the intensity based approach, where the propensity of prepayment or calling is modeled by the intensity of a Poisson process. We illustrate that the corresponding pricing formulation resembles the penalty approximation approach commonly used in the solution of the linear complementarity formulation of an optimal stopping problem. We obtain several theoretical results on the prepayment strategies of mortgage loans and calling policies of American warrants. We also propose robust second order accurate numerical schemes for solving the penalty formulation of an optimal stopping problem. (C)2007 Elsevier B.V. All rights reserved.

Published
2007

6. Intensity-based framework and penalty formulation of optimal stopping problems

Abstract

Financial derivatives commonly contain premature termination clauses, which are embedded rights held by the holder or writer. Well known examples of these stopping rights include the early exercise right in American options, the callable right in callable securities and the prepayment right in mortgage loans. In this paper, we show how to model the mortgagor's prepayment in mortgage loans and the issuer's call in the American warrant as an event risk using the intensity based approach, where the propensity of prepayment or calling is modeled by the intensity of a Poisson process. We illustrate that the corresponding pricing formulation resembles the penalty approximation approach commonly used in the solution of the linear complementarity formulation of an optimal stopping problem. We obtain several theoretical results on the prepayment strategies of mortgage loans and calling policies of American warrants. We also propose robust second order accurate numerical schemes for solving the penalty formulation of an optimal stopping problem. (C)2007 Elsevier B.V. All rights reserved.

Published
2007

7. Intensity-based framework and penalty formulation of optimal stopping problems

Abstract

Financial derivatives commonly contain premature termination clauses, which are embedded rights held by the holder or writer. Well known examples of these stopping rights include the early exercise right in American options, the callable right in callable securities and the prepayment right in mortgage loans. In this paper, we show how to model the mortgagor's prepayment in mortgage loans and the issuer's call in the American warrant as an event risk using the intensity based approach, where the propensity of prepayment or calling is modeled by the intensity of a Poisson process. We illustrate that the corresponding pricing formulation resembles the penalty approximation approach commonly used in the solution of the linear complementarity formulation of an optimal stopping problem. We obtain several theoretical results on the prepayment strategies of mortgage loans and calling policies of American warrants. We also propose robust second order accurate numerical schemes for solving the penalty formulation of an optimal stopping problem. (C)2007 Elsevier B.V. All rights reserved.

Published
2007

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