Positional Option Trading. Euan Sinclair

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Название Positional Option Trading
Автор произведения Euan Sinclair
Жанр Ценные бумаги, инвестиции
Серия
Издательство Ценные бумаги, инвестиции
Год выпуска 0
isbn 9781119583530



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realized volatility (which determines the rebalancing profits). This is true no matter which structure is chosen and the particulars of the hedging scheme.

      If we can identify situations where this volatility mismatch occurs, the expected profit from the position will be given by

      This is the fundamental equation of option trading. All the “theta decay” and “gamma scalping” profits and losses are tied up in this relationship.

      Note also that this vega P/L will affect directional option trades. If we pay the wrong implied volatility level for an option, we might still make money but we would have been better off replicating the option in the underlying.

      The BSM equation depends on a number of financial and mathematical assumptions.

       The underlying is a tradable asset.

       There is a single, risk-free interest rate.

       The underlying can be shorted.

       Proceeds from short sales can be invested at the risk-free rate.

       All cash flows are taxed at the same rate.

       The underlying's returns are continuous and normally distributed with a constant volatility.

      The IV surface exists partially because the BSM is mathematically misspecified. The underlying does not have returns that are continuous and normally distributed with a constant volatility. However, even a model that perfectly captured the underlying dynamics would need a fudge factor like the implied volatility surface. Some of the reasons for its existence have nothing to do with the underlying. Different options have different supply and demand, and these distort option prices. Because of this, there is often an edge in selling options with high volatilities relative to others on the same underlying (see the section on the implied skewness premium in Chapter Four).

Graph depicts the implied volatility surface for SPY on September 10, 2019. Graph depicts the terminal PL distribution of a single short one-year ATM straddle that is never re-hedged. Stock price is $100, rates are zero, and both realized and implied volatilities are 30 percent. Graph depicts the terminal PL distribution of a single one-year ATM straddle that is hedged daily. Stock price is $100, rates are zero, and both realized and implied volatilities are 30 percent. Graph depicts the standard deviation of the terminal PL distribution of a single one-year ATM straddle as a function of the number of hedges. Stock price is $100, rates are zero, and both realized and implied volatilities are 30 percent.

      The difference between these two cases is roughly equivalent to misestimating volatility by two points.

       TABLE 1.1 Statistics for the Short One-Year ATM Daily Hedged Straddle With and Without Hedging Costs (stock price is $100, rates are zero, and both realized and implied volatilities are 30%.)

Statistic Costless Hedges $.10/Share Hedges
Average −$6.10 −$121.54
Median −$49.85 −$111.68
Percent profitable 44% 30%

      The