Bilateral Multiple Gamma Returns: Their Risks and Rewards

Madan, Dilip B.; Schoutens, Wim; Wang, King

doi:10.2139/ssrn.3230196

Cited by 11 publications

(9 citation statements)

References 53 publications

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“…This model extends the variance gamma model by modelling the speed of positive and negative jumps separately. More generalizations and extensions consist in imposing the model parameters themselves to be gamma distributed, as explained in Madan et al (2018). We consider one such model, the bilateral double gamma (BDG) model.…”

Section: Gamma Modelsmentioning

confidence: 99%

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Advanced model calibration on bitcoin options

2019

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In this paper, we investigate the dynamics of the bitcoin (BTC) price through the vanilla options available on the market. We calibrate a series of Markov models on the option surface. In particular, we consider the Black-Scholes model, Laplace model, five variance gamma-related models and the Heston model. We examine their pricing performance and the optimal risk-neutral model parameters over a period of 2 months. We conclude with a study of the implied liquidity of BTC call options, based on conic finance theory.

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Section: Gamma Modelsmentioning

confidence: 99%

“…The bilateral double gamma model (Madan et al 2018) goes one step further in the generalization by allowing the speed parameters c p and c n to vary randomly. They are assumed to be gamma distributed, with characteristic functions:…”

Section: The Bilateral Double Gamma Modelmentioning

confidence: 99%

Advanced model calibration on bitcoin options

2019

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“…Some other examples are presented in Barndorff-Nielsen (1998), and Eberlein and Keller (1995). More recently, Madan et al (2018) argue that for a maximal entropy time change the time change should follow a gamma distribution and this delivers the variance gamma model of Madan and Seneta (1990). It was already observed in Madan and Seneta (1990) that the variance gamma model is a difference of two independent gamma processes each separately modeling the upward and downward motion of markets.…”

Section: Modeling Transition Ratesmentioning

confidence: 95%

“…The difference of two gamma processes with differing scale and speed on both sides is referred to as the bilateral gamma model as first introduced in Küchler and Tappe (2008). Madan et al (2018) also note that maximal entropy considerations for upward and downward motions suggest gamma process models for the two sides. These considerations suggest the use of a four parameter bilateral gamma model for the local motion of the logarithm of the asset price.…”

Section: Modeling Transition Ratesmentioning

confidence: 99%

Arbitrage Free Approximations to Candidate Volatility Surface Quotations

Madan

Schoutens

2019

JRFM

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It is argued that the growth in the breadth of option strikes traded after the financial crisis of 2008 poses difficulties for the use of Fourier inversion methodologies in volatility surface calibration. Continuous time Markov chain approximations are proposed as an alternative. They are shown to be adequate, competitive, and stable though slow for the moment. Further research can be devoted to speed enhancements. The Markov chain approximation is general and not constrained to processes with independent increments. Calibrations are illustrated for data on 2695 options across 28 maturities for S P Y as at 8 February 2018.

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“…We take mean reverting processes for r and λ. Randomness of the rate r is represented by a gamma process g r , whereas for λ it is the sum of a double gamma process g λ • g τ and a scalar multiple ρ of g r itself. Multiple gamma processes were first investigated in Madan et al (2020), for the purpose of randomizing the speed at which jumps occur. To our knowledge, ours is the first application of a pure jump process with infinite arrival rate in credit risk modeling.…”

Section: Introductionmentioning

confidence: 99%

A pure jump model for the valuation of options on a credit index

Shirai¹

2023

Preprint

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A two dimensional pure jump process is proposed to model the evolution of the risk free rate and default intensities for the purpose of evaluating option contracts on a credit index. Time evolution in credit markets is assumed to follow a gamma process evaluated at calendar time in order to reflect different levels of business activity in the credit and Treasury markets, which ultimately reflect differences in preferences and incentives of credit products investors, as well as the structure of the credit market itself, with those of their respective counterparts in the Treasury market. Formulas for the characteristic function, zero coupon bonds and moments of the process are derived, and its parameters calibrated to market prices of options on a credit index. Model and market implied credit spreads moments are estimated and compared.

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Bilateral Multiple Gamma Returns: Their Risks and Rewards

Cited by 11 publications

References 53 publications

Advanced model calibration on bitcoin options

Advanced model calibration on bitcoin options

Arbitrage Free Approximations to Candidate Volatility Surface Quotations

A pure jump model for the valuation of options on a credit index

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