### Table IV Performances of the Genetic Programming Model and the Black-Scholes Model in a Jump-Diffusion World We generate the underlying stock price as a jump-diffusion process. The model specifications for Genetic Programming are specified in Table IV. Pricing errors are presented for six Genetic Programming algorithms that use alternate methods for generating new populations from the previous generation. Each cell in the table presents the average pricing-error over the entire sample of options generated in each sample set. Parent Selection Criteria: Best Mean Absolute Error Mean Percentage Error

1998

Cited by 7

### TABLE 4. Call option price and sensitivities for a jump di usion process. This table lists results for the option price and its input parameter sensitivities when a jump process is superimposed on the continuous process of the Black-Scholes model. Initial stock value is set to S = 100 and the strike price is X = 100. Number of Monte Carlo steps is 1 105. Each Monte Carlo result is immediately followed by its error estimate . Jump rate per period is set to kP = 0:1. Riskless interest rate per period is rf = 0:004853 and variance per period is 2 = 0:001875. Jump sizes are uniformly distributed in the interval (? ;+ ). is the stock price sensitivity ( = @C=@S), is the volatility sensitivity ( = @C=@ ), and is the interest rate sensitivity ( = @C=@rf).

1994

### Table 7: Left: a price jump of factor 0.11 from date 2 to 3; right: the corrected table

2007

"... In PAGE 28: ...he price jumps have approximately the factors 0.01, 0.1, 10 or 100, because actual stock prices also change from date to date. For instance, in Table7 , the price jump has factor 0.11, but should be corrected by applying a factor 10.... ..."

### Table V Performance of Genetic Programming Model, Black-Scholes Model, and Linear Models in a Jump-Diffusion World Pricing errors are presented for six Genetic Programming formulas using alternate methods for generating new populations from the previous generation and for four linear models that are a function of the initial stock price, exercise price, and time to maturity. Each cell in the table presents the average pricing errors over ten sets of stock and option prices and for the entire sample of options generated in each set. Parameter values used to generate stock price and options data and the Genetic Programming parameters are given in Table IV.

1998

Cited by 7

### Table 5: Prices of Lookback Call Options n28Monthly Frenquencyn29. S = 20, SM =

1997

"... In PAGE 15: ... Based on this theorem, a numerical approach similar to the one used to value barrier options can be used to value lookback options. Table5 presents a numerical example to illustrate the en0bects of jumps on lookbacks. In this table, the volatility of stock price n1b 2 S is n0cxed at a constant level 0:01.... ..."

### Table 1. Percentage Change in Stock Price Index

"... In PAGE 7: ... Starting sometime in the second half of the 1980s, rapid expansion was accompanied by sharp increases in asset values, notably stock and land prices. As shown in Table1 , since 1987, stock price indices increased rapidly in East Asia. Among the economies more affected by the recent crisis the highest cumulative price increases were in Indonesia (934 percent), Thailand (702 percent) and the Philippines (556 percent).... In PAGE 7: ... After the second half of 1997, the value of the most affected East Asian currencies had fallen 33%-75% against the US dollar. Table1 reveals that stock indices also declined sharply after June 1997, falling 36 percent in Indonesia, 43 percent in Korea... ..."

### Table 9. Average Put and Call Prices on the Stock

in Abstract

2007

"... In PAGE 23: ... A put-call parity relationship holds for these options, but the formula is awkward because of the stochastic dividend stream. Table9 shows for both the LRR and HAB models the unconditional means of the implied relative call and put prices written on the dividend asset Pdt. The expiration dates range from one through twelve months ahead and the strike-to-underlying ratios are 0.... In PAGE 23: ... The average put prices might seem high relative to the average call prices but one must keep in mind the dividend, which tends to increase the value of puts relative to calls. Overall, the average prices shown in Table9 exhibit the usual properties of call and put options. There does not seem to be... ..."

### Table 9. Average Put and Call Prices on the Stock

"... In PAGE 23: ... A put-call parity relationship holds for these options, but the formula is awkward because of the stochastic dividend stream. Table9 shows for both the LRR and HAB models the unconditional means of the implied relative call and put prices written on the dividend asset Pdt. The expiration dates range from one through twelve months ahead and the strike-to-underlying ratios are 0.... In PAGE 23: ... The average put prices might seem high relative to the average call prices but one must keep in mind the dividend, which tends to increase the value of puts relative to calls. Overall, the average prices shown in Table9 exhibit the usual properties of call and put options. There does not seem to be... ..."

### Table 1 Poisson jump-di usion parameter estimates for the DAX across di erent subperiods (Standard errors in parentheses) Panel A: Daily returns

1995

"... In PAGE 10: ... A weekly rate of return is de ned as the di erence between the logarithm of two successive Wednesday prices. Table1 summarizes the Poisson jump-di usion parameter estimates for the DAX stock in- dex returns across di erent subperiods. In addition to the ve parameters to be estimated (instantaneous mean D and variance 2 D of the di usion component, the mean number of abnormal information arrivals (jumps) per unit time , the mean J and variance 2 J of the (logarithmic) jump size) the table reports on the annualized total standard de- viation (volatility) of the jump-di usion process (VOLA)8, the log-likelihood value and the likelihood ratio test statistic ( ).... ..."

Cited by 2