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A question you may be asked during a quantitative finance interview... ——————————————————————— Why a straddle is not a pure bet on volatility? ——————————————————————— A straddle is an options strategy that involves buying both an at-the-money (ATM) call option and an ATM put option on the same underlying asset with the same strike price (K) and expiration date. The straddle holder profits from significant price movements in either direction, as the combined positions in the call and put options will yield a profit if the underlying asset's price moves significantly above or below the strike price. Initially, when the stock price (S) is close to the strike price (K), the delta of the straddle is approximately 0. Why? The delta of an options position measures the rate of change of the option's price with respect to changes in the underlying asset's price. For a single call option or put option, the delta ranges from -1 to 1, indicating the sensitivity of the option's price to the movement of the underlying asset's price. However, in the case of a long straddle, where an investor buys an at-the-money (ATM) call option and an ATM put option with the same strike price (K) and expiration date, the deltas of the call and put options have opposite signs and magnitudes of 0.5 each. This is because an ATM option typically has a delta close to 0.5 for both calls and puts, as it is equally likely to end up in the money or out of the money at expiration. When you combine the deltas of the long call and long put in a straddle, the result is 0.5 (from the call option) minus 0.5 (from the put option), which gives an initial delta of 0 for the straddle position. A delta close to 0 implies that the straddle's value does not change significantly with small movements in the stock price. As a result, the straddle is considered market-neutral or delta-neutral, as it is not strongly exposed to stock price movements. However, as the stock price moves away from the strike price, the delta of the straddle changes. The call option's delta increases as the stock price rises, while the put option's delta increases as the stock price falls. As a result, the straddle's overall delta becomes less close to 0, and the strategy becomes more exposed to stock price movements in either direction. While a straddle allows investors to profit from large price swings in the underlying asset, it is not a pure bet on stock volatility. The potential profit from a straddle comes from both price movements and changes in implied volatility, as volatility affects the option prices. The investor's exposure to stock price movements limits the strategy's effectiveness as a pure play on volatility. For a pure bet on volatility, investors can use volatility swaps or variance swaps. #QuantFinanceInterviewQuestion #StraddleStrategy #OptionsTrading #DeltaNeutralStrategy #VolatilityBet #ImpliedVolatility #VarianceSwaps #OptionPricing