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 of $100.

The exchange-listed Vix-based derivatives include futures contracts, which began trading in 2004, and call and put options on the Vix, which began trading in February 2006. The final settlement date of the Vix futures contract is the third Wednesday of each month. Typically, there are listed futures contracts with a settlement date up to six near-term months and a few longer-term contracts. The underlying of the Vix call and put options is the Vix spot value observed on the option expiry date, which is specified in the same way as the settlement day for futures contracts. The Vix options are of European exercise style.

[image] - Vix option pricing in a jump-diffusion model (PDF, 338KB)