Pricing, Hedging, and Calibration in Jump‐Diffusion Models

Tankov, Peter; Voltchkova, Ekaterina

doi:10.1002/9781118266915.ch5

Cited by 2 publications

(1 citation statement)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To summarize, jump-diffusion models shed light on an explanation of the implied volatility smile phenomenon as the implied volatility is different from the historical volatility as well as varies as a function of strikes (see Tankov et al [34]). Our observations meet our expectations concerning Figure 5, which shows possible implied volatility patterns (as a function of strikes) in the Merton-Bates jump-diffusion model.…”

Section: Numerical Applicationmentioning

confidence: 99%

Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging

Chen

Huang

2021

Mathematics

View full text Add to dashboard Cite

In this paper, we conduct a fast calibration in the jump-diffusion model to capture the Bitcoin price dynamics, as well as the behavior of some components affecting the price itself, such as the risk of pitfalls and its ambiguous effect on the evolution of Bitcoin’s price. In addition, in our study of the Bitcoin option pricing, we find that the inclusion of jumps in returns and volatilities are significant in the historical time series of Bitcoin prices. The benefits of incorporating these jumps flow over into option pricing, as well as adequately capture the volatility smile in option prices. To the best of our knowledge, this is the first work to analyze the phenomenon of price jump risk and to interpret Bitcoin option valuation as “exceptionally ambiguous”. Crucially, using hedging options for the Bitcoin market, we also prove some important properties: Bitcoin options follow a convex, but not strictly convex function. This property provides adequate risk assessment for convex risk measure.

show abstract

Section: Numerical Applicationmentioning

confidence: 99%