Case analysis: pricing 4 June 2024

India VIX is the market's 30-calendar-day implied volatility of Nifty, annualised on a 365-day basis. It closed at about 24.6 on 31 May 2024 (before the exit polls) and 20.94 on 3 Jun 2024 (after the exit-poll rally; Yahoo ^INDIAVIX series). Realised Nifty daily volatility over January–May 2024 was 0.72%. Assume a 30-calendar-day window contains 21 trading days, one of which is the result day. (a) From VIX = 24.6, compute the 30-day implied variance and standard deviation. Assuming the 20 ordinary days each have variance $(0.72\%)^2$, back out the implied standard deviation of the result day. (b) Repeat (a) with VIX = 20.94. (c) The realised result-day log return was $-6.1\%$. Express it in standard deviations of (i) an ordinary day and (ii) the implied result day from (b). (d) Model the result-day return as $X + \sigma\varepsilon$ with $\sigma = 0.72\%$, $X = +a$ with probability $\pi$ and $X = -b$ with probability $1 - \pi$, and $E[X] = 0$. Using (b), find the $\pi$ for which $b = 6.1\%$, and the corresponding $a$. (e) Discuss what (a)–(d) say about how the event was priced, and list at least three reasons why option-implied variance overstates the physical-probability event variance or why the two-point model misleads.