"... In PAGE 12: ... The value of e vt is, in this case, close to zero, indicating a situation in which the market is fairly liquid and there is not any unbalances between demand and supply. Since illiquidity is mostly associated to sudden price drops accompanied by tiny volume, the Illiquid Market in Table1 represents a situation in which the index falls by 3.6% and volume is at the minimum in the analyzed sample.... ..."

"... In PAGE 19: ... The other parameter setting are the same as the case of partial average Asian call options. The numerical results (based on 50,000 independent replications) in Table9 (BS indicates the true Black-Scholes price) indicate that indirect estimation via put-call parity can e ectively reduce the estimation variance in pricing in-the-money call options. When combined with importance sampling, we obtain tremendous variance reduction, nearly ve orders of magnitude in the best case of our simulation experimental testbed.... ..."

"... In PAGE 13: ...Table 2 Option: European put S = 100:0; K = 100:0; T = 10; Model: Merton jump-di usion = 0:15; = 0:1; ~ = 1:08; ~ = 0:4; r = 0:05; q = 0:02; Closed-Form Price: 18:003629 Quoted Price: 18:0034 Source: Andersen and Andreasen (2000) We use estimates of the option price vapprox on successively ner grids in space to establish the rate of convergence via px = log2 jvapprox( x) vapprox( x=2)j jvapprox( x=2) vapprox( x=4)j: (21) Here, the absolute changes in the numerator and the denominator are given in the table un- der the column \Change quot;, while the estimated rate of convergence is given under the column \log2Ratio quot;. For European options under various processes (see Table2 and Tables 7 - 9 in Appendix A) we nd that the FST algorithm is order 2 in the space variable. For path dependent options it is also necessary to establish convergence properties of the algorithm in the time variable.... ..."

"... In PAGE 3: ... 2 Numerical comparison In this section we will compare some well known methods for barrier option valuation with our closed form solution method. Table1 compares European barrier option values. Column one is calculated using the closed form barrier formulas derived by Reiner and Rubinstein #281991#29.... ..."

"... In PAGE 11: ... Also, other numerical experiments reported in Laprise (2002) indicate only linear growth in the computation time of our algorithm with the number of exercise dates. Analogous to Table 1, Table2 shows the results of applying the secant and tangent algorithms to a put option with the same parameters as for the call, except for the dividend rate set to zero. The row labeled Eur displays the corresponding European put prices given by (19) and (24) with SLeta = 3periodori0.... ..."

"... In PAGE 11: ...1 International Comparison Analysis The accuracy rate and AUROC results of the five modelling approaches in different countries over the 5 year period are given in table 3. Table3 Model Performance in Target Markets USA Market Methodology Performance Measures 2004 2003 2002 2001 2000 Average Accuracy Rate (%) 89.76 90.... ..."

"... In PAGE 15: ... Then using an argument similar to the one after the proof of The- orem 2 in the Appendix, the strong maximum principle implies that portfolio process t of (8) satis es t lt; u for t lt; T . Numerical results for European call options are given in Table1 . To be speci c, consider the case with K = 100 and = 0:3.... ..."

"... In PAGE 13: ...10 Numerical results for four di erent types of options are given in Table2 . For American calls to have value in excess of their European counterparts, a constant dividend rate of = 10% is used.... ..."