### Table 2: Asian Option Pricing Confidence Intervals

### Table 1: Asian Option Pricing Simulation

### Table 2: Asian Option Pricing Confidence Intervals

### Table 2: Asian call options: S

2002

"... In PAGE 16: ...0.2;;r=0.05, T =1.0yr, =0.001, N 1 =20, N 2 =50. From Table2 , we see that our algorithm converges very fast, coming very close to the optimal value using less than 1000 simulations, where N 1 is the actual # of iterations used in optimization stage. Comparison Between Importance Sampling and Naive Simulations Asian Options on Partial Average In this testbed, the stock price again follows geometric Brownian motion as given by (22), with payo function de ned by (23).... ..."

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### Table 2: MC Results: Simulated Prices of the Asian Basket Options using Random Sequences

2003

"... In PAGE 9: ...rices for the zero and positive correlation cases are 3.4409 and 5.6490 with standard errors of 0.0044 and 0.0082, respectively. One immediate conclusion from Table2 is that there is no significant difference among the various construction approaches. This is not surprising since the rate of convergence of Monte Carlo methods does not depend on dimensions as well as the decomposed matrix ~ C.... ..."

### Table 3: QMC results: Simulated Prices of the Asian Basket Options using Randomized Low Discrepancy Sequences

2003

"... In PAGE 9: ... This is not surprising since the rate of convergence of Monte Carlo methods does not depend on dimensions as well as the decomposed matrix ~ C. In Table3 , the same set of examples and the same techniques are compared. The only difference is that the input is drawn from the randomized Sobol0 low discrepancy sequences proposed by Owen (1995), instead of a random sequence.... ..."

### Table 7: Geometric Asian Options Pricing using Biased amp; Unbiased Control Variates [r = 0:09; = 0:2; S0 = $100; T = 0:4yrs, #replications: 10,000] Unbiased Biased Unbiased Biased

1997

"... In PAGE 16: ...ere just the control volatilities of .19 and .21 since the results are similar. Table7 presents the results. The column labeled \Cont.... In PAGE 17: ... Our ndings raise questions for future research into the design of appropriately biased control variates for particular classes of problems. 4The standard errors with these control variates in Table7 were below .0035.... ..."

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### Table 1: Asian call options: S

2002

"... In PAGE 29: ...189 7.841 Table1 0: European Asian Calls, S 0 =100, T =1yr, =r for Naive.... ..."

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### Table 4: Estimated variance reduction factors w.r.t. MC for the Asian-option example

2000

"... In PAGE 27: ... When we combine CV with IS and COND, we rst generate the vector (Z1; : : : ; Zt) using COND, then apply IS to generate the price of both options (on the arithmetic and geometric average), and nally use CV. Table4 reports the estimated variance reduction factors with respect to MC, for cer- tain combinations of the methods. The parameters of the option are = 0:3, r = 0:05, K = 55, S(0) = 50, T = 1 year and t = 64.... ..."

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