![]() ![]() For the other options, when volatility is 0, the extrinsic value is clearly 0.This is represented by the red line above. (Actually, it is slowly decreasing as volatility increases, but not noticeably so). Differentiating the straddle approximation formula with respect to volatility, we see that the ATM vega is pretty constant.Let's consider the graph of vega against volatility:Įxplanation for characteristics of the above graph: This backs up the observation made in the previous section. Thus, the vega of the straddle is positive, which implies that the vega of the individual options is positive. As volatility increases, we are likely to see larger moves in the underlying, which will result in a higher payoff as the underlying moves away from the strike. Thus, to know the vega of an option on a strike, we can consider either the call or the put option, or even consider the case of the straddle!įor example, let's consider the vega of a straddle. This tells us that the vega of the call and the put on the same strike and expiration is the same. \nu_C - \nu_P = 0 \Longrightarrow \nu_C = \nu_P. ![]() The put-call parity states that C − P = S − K e − r t C - P = S - K e^ K e − r t are independent of volatility, the RHS is 0. In the above example, because the vega of an ATM option is mostly constant, the approximation is extremely accurate. This would be accurate as a first-order approximation. The above example shows how knowing the vega of an option allows us to calculate the price change which results from a volatility change. Since the vega of the option is 0.056, our best guess of the option value is that it has increased by 8 × 0.056 = 0.448 8 \times 0.056 = 0.448 8 × 0. The volatility has increased by 70 − 62 = 8 70 - 62 = 8 7 0 − 6 2 = 8 vol points. If the vega of the option is 0.056, what would be the price of the option when implied volatility is 70? When the stock is trading at $45, the call option on the $45 strike with 25 days to expiry is worth $3.48 at an implied volatility of 62. It allows us to make predictions about how much the option value would change as volatility changes. The vega of an option tells us how much the price of an option would increase by when volatility increases by 1%. ![]()
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