### Table 2: Parameters for Correlated Brownian Motions

2003

"... In PAGE 22: ...Valuation Under Different Price Models We first examine the effects of price model specification on power plant valuation for two different price processes: a geometric Brownian motion (GBM) process and a mean-reverting process in which the logarithm of the underlying price is represented by an Ornstein-Uhlenbeck (O-U) process. The assumed parameter values for the two models are given in Table2 and Table 3. A discrete-... In PAGE 22: ...Table 2: Parameters for Correlated Brownian Motions time trinomial price lattice is constructed according to (3) and (4) with the parameters specified in Table2 to approximate two correlated GBMs and a quadrinomial lattice is constructed according to (6) and (9) with the parameters in Table 3 to approximate two correlated O-U processes. The initial prices of electricity and natural gas are assumed to be $21:7 per MWh and $3:16 per MMBtu, which are sampled from historical market prices.... In PAGE 23: ...0% GBM Valuation MRVT Valuation ABS(MRVT-GBM)/MRVT Figure 2: Value of a NG fired Power Plant under Alternative Price Models: GBM vs. Mean- reversion The parameters specified in Table2 and Table 3 were selected so that the asset values VGBM and Vmrvt would match if the power plant has a heat rate of Hr = 9:5 (which is typical for a NG fired plant) and it is operated at the maximum capacity level. Figure 2 illustrates the sensitivity of plant value to the assumed price process.... In PAGE 25: ... The time horizon is set to be 10 years. Again we use the parameter values given in Table2 and 3. 4.... ..."

Cited by 1

### Table I Parameters for Brownian Motion

### Table I Parameters for Brownian Motion

### Table 4. Value of the option to grow depending on the number of discrete jumps Initial project demand is 10 million of physical units, market share is 50%, unitary margin is one monetary unit, and life span is 5 years. We assume complete capital markets and a risk-free rate of 6%. The option to grow is a quasi-American type call option, which can be exercised at the end of the second, third and fourth years. Its exercise implies an outlay of the 20% of initial investment, and it increases the project sales by 50% of the existing level. Option values are estimated by both Critical values proposal and Regression proposal. Regression I uses the same simulated paths to estimate the optimal exercise strategy and the option value, whereas the Regression II employs different sets of simulations. We consider a mixed Brownian-Poisson process. Geometric-Brownian drift is 15%, with alternative volatilities of 10%, 20% and 30%. For the jump motion, we consider a range of volatilities between 25% and 500%, with an average number of annual jumps ranging of 0.20 to 1. The number of simulated paths, H, is 400,000 (200,000 from direct approximations plus 200,000 antithetical estimations. M and K in the critical value proposal are equal to 400.

2005

### Table 10 The first two moments for seven Brownian areas.

"... In PAGE 48: ... 28. A comparison For easy reference, we collect in Table10 the first two moments of the various Brownian areas treated above, together with the scale invariant ratio of the second moment and the square of the first. Note that the variables Bex, Bdm, Bme, Bbr, Bbm have quite small variances; if these variables are normalized to have means 1, their variances range from 0.... ..."

### Table 1: Exact results vs. Brownian bridge, N = 100

2004

### TABLE 1 Range of rate constants for the Brownian ratchet and power stroke models

### TABLE III: Brownian motion model tted to each of the ve exposures.

### Table 2 Bermudan Put Option on Asset Under Geometric Brownian Motion

"... 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.... ..."

### Table 1: Monte Carlo critical values for the test statistic (N=2)12 D, using the Haar wavelet lter, for a level test. These values are based upon 10,000 replicates. The standard error (SE) is provided for each estimate, and was computed via SE = f (1 ? )=(10; 000f2)g1 2 where f is the histogram estimate of the density at the (1? )th quantile using a bandwidth of 0 01 (Incl an amp; Tiao, 1994). Quantiles of a Brownian bridge process are given at the far right for comparison.

1400

"... In PAGE 6: ...39) of Billingsley (1968). Table1 shows how quickly the Monte Carlo critical values converge to the quantiles of the Brownian bridge process. 3 2 Simulation study To study if in fact the discrete wavelet transform of a fractional di erence process is a good approximation to white noise as far as performance of the test statistic D is concerned, we determined the upper 10%, 5% and 1% quantiles for the distribution of D based upon 40,000 realizations of samples of white noise for a range of sample sizes commensurate with time series of sample sizes N 2 (128; 256; 512; 1024; 2048).... In PAGE 7: ... One may not want to perform Monte Carlo studies in order to obtain critical values for the test statistic D. The simulation study described above was run again substituting the asymptotic critical values (last column of Table1 ) for the Monte Carlo critical values. For sample sizes greater than 128 the percentage of times D exceeded the asymptotic critical... ..."