Question

Consider the situation where the maximum temperature in degrees Farenheit for the seven successive days in a certain week is the vector random variable, (T1,..., T7), where T1~U(70; 80); Tj+1 = 14 + 0:8Tj + 3Xj ; j = 1,...6; where X1,...,X6 i.i.d. N(0; 1). A weather derivative pays $100 if there are two or more days with maximum temperatures below 70 degrees. Using Monte Carlo simulation in R, compute the fair price of this derivative with relative error of no more than 1%.

Answer 1

Solution:

Using Monte Carlo simulation in @RISK Software the following working is shown:

The fair price of this derivative is $36.42.

Further summary is as below:

Name	Expected payoff/Maximum Temperature	Normal	T1 Uniform
Description	output	Risk Normal(0,1)	Risk uniform(70,80)
Cell	Sheet1!B14	Sheet1!B2	Sheet1!B3
Minimum	0.00	-3.994507	70.00043
Maximum	100.000	3.821233	79.99939
Mean	36.400	-8.81336E-06	75
std Deviation	48.117	0.9999822	2.886891
Variance	2315.271	0.9999643	8.334138
Skewness	0.5653987	-0.000514297	-8.52046E-07

Kurtosis

1.31934

2.996927

1.799999