underlier


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underlier

[′ən·dər‚lī·ər]
(mining engineering)
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The first result for the random draw from the returns distribution of the underlier is a comparatively high 3.98 percent, producing a subsequent price for the underlying asset at T = 30 of $51.99.
Table 1 reports the call options returns statistics by moneyness and time to maturity when all the assumptions of Black-Scholes hold: the returns of the underlier are normally distributed and volatility is constant.
This beta is not to be confused with the standard option delta, which measures the sensitivity of the option price to changes in the price of the underlier. A similar statistic, [[beta].sub.C/S], is calculated later for put options.
Table 2 reports the put options returns statistics by moneyness and time to maturity when all the assumptions of Black-Scholes hold: the returns of the underlier are normally distributed and volatility is constant.
Therefore, the two sub-periods provide a great opportunity to study the effect on realized option returns of non-normality in the returns of the underlier. Table 3 presents the returns statistics for the S&P 500 Index returns over the relevant period.
The average returns reported are for 30,000 simulated scenarios of the underlier's price.
Interestingly, the large losses are confined to the short-dated 30-day calls, as longer-dated OTM calls do not exhibit this pattern with bull market underlier returns.
In other words, a high-volatility environment is required for skewness in the returns of the underlier to produce call returns which match the pattern documented empirically.