Consider the following form of the BlackScholes equation: where V (S,) is the option price and S

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Consider the following form of the Black–Scholes equation: 

aw 02 2W 2 2 2 -  = + (r-q- 0) aw 2 ax W = e-rtV and x = In S,

where V (S,τ) is the option price and S is the asset price. The two-level sixpoint implicit compact scheme takes the form: 

aj Wn+1 j+1 + aow

where 

c=(r-q-27) 4- an = 1  3  3  a-1 = 1  3 + 3c bo = 10  6 - 2c 2 - 2 - M + - n = 0   2  4x2 ao = 10 + 6 + b1 = 1

Show that the compact scheme is second-order time accurate and fourth order space accurate.

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