Vix option pricing in a jump-diffusion model

Artur Sepp discusses Vix futures and options and shows that their market prices exhibit positive volatility skew. To better model the market behaviour of the S&P 500 index and its associated volatility skew, he introduces the stochastic dynamics of the volatility of the S&P 500 index with volatility jumps. Then he develops closed-form solutions for unified pricing of options on the S&P 500 index and its volatility

The Chicago Board Options Exchange (CBOE) Volatility Index (Vix) measures the implied volatility of S&P 500 stock index options with a maturity of 30 days. In a broad sense, the Vix represents the market expectation of the annualised at-the-money (ATM) implied volatility over the next 30-day period. The Vix spot value is calculated by the CBOE minute-to-minute using real-time bid/ask market quotes of S&P 500 index (SPX) options with nearby and second nearby maturities and applying the multiplier