Random Time Forward-Starting Options

Antonelli, Fabio; Ramponi, Alessandro; Scarlatti, Sergio

doi:10.1142/s0219024916500503

Cited by 4 publications

(1 citation statement)

References 27 publications

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“…Assuming that B(t, •)Z. is a bounded F− martingale (which is usually the case), we can treat the expectation in (4), applying an extension of Proposition 5.1.1 of [6], as developed in [3].…”

Section: Cva Evaluation Of Defaultable European Claimsmentioning

confidence: 99%

Cva and Vulnerable Options in Stochastic Volatility Models

Alòs

Antonelli

Ramponi

et al. 2021

Int. J. Theor. Appl. Finan.

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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.

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Section: Cva Evaluation Of Defaultable European Claimsmentioning

confidence: 99%

Cva and Vulnerable Options in Stochastic Volatility Models

Alòs

Antonelli

Ramponi

et al. 2021

Int. J. Theor. Appl. Finan.

Self Cite

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CVA and vulnerable options pricing by correlation expansions

2019

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We consider the problem of computing the Credit Value Adjustment (CVA) of a European option in presence of the Wrong Way Risk (WWR) in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in [2]. We compare the numerical performance of such a method with that recently proposed by Brigo et al. ([8], [10]) in the case of a call option driven by a GBM correlated with the CIR default intensity. We additionally report some numerical evaluations obtained by other methods.

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