MAT1856S/ APM466S
Mathematical Theory of Finance - Assignment 2
Due March 8, 2021
Gasoline prices are at p0 = $1/litre today, and each week i the price
can go up by 10% to pi+1 = pi · 1.1 with probability 50%, or down to
pi+1 = pi/1.1 also with probability 50%.
Mr. Hamilton drives a car and each week consumes 50 litres of gasoline.
He purchases price protection insurance in the form of a 4-upswing option
with strike price $1, which works as follows:
1 . On a given week, he can exercise one purchase option for 50 litres
(no more nor less) at a fixed price of $1/litre.
2 . He can exercise this purchase option a maximum of 4 times in a given
year.
On the other hand, Ms. Curie runs a refinery, and produces 50,000
litres of gasoline every week, that she sells at market prices. She will pur-
chase a price protection program in the form of a 4-downswing option which
works as follows:
1 . On a given week, she can exercise one sell option for 50,000 litres (no
more nor less) at a fixed price of $1/litre.
2 . She can exercise this purchase option a maximum of 4 times in a
given year.
In both cases, using recombining trees, calculate the price of the price
protection plan in each case, as well as the optimal exercise nodes in the
option trees.
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