No Arbitrage 1. Consider the following three securities: SNOW, RAIN and SUN. SNOW pays $100 if it snows on NYU graduation day. RAIN pays $100 if it rains, but doesn’t snow on NYU graduation day. SUN pays $100 if there is neither rain nor snow on graduation day. Suppose that SNOW is currently trading at $1, RAIN is currently trading at $41 and SUN is trading at a price of $52. (a) If you buy 1 share of SNOW, 1 share of RAIN and 1 share of SUN, what is the payoff you guarantee on NYU graduation day? (b) According to the No Arbitrage Condition, what must be the price of a $100 face value zero-coupon bond that matures on NYU graduation day? (c) Suppose that this zero-coupon bond is trading at $90. How would you set up a transaction to earn a riskless arbitrage profit? Assume no trading costs. (d) Suppose that trading zero-coupon bonds and RAIN is costless, but shorting SUN costs $3 per $100 face value and shorting SNOW costs $1 per $100 face value. Can you still make an arbitrage profit?
No Arbitrage
1. Consider the following three securities: SNOW, RAIN and SUN. SNOW
pays $100 if it snows on NYU graduation day. RAIN pays $100 if it rains, but doesn’t
snow on NYU graduation day. SUN pays $100 if there is neither rain nor snow on
graduation day. Suppose that SNOW is currently trading at $1, RAIN is currently
trading at $41 and SUN is trading at a price of $52.
(a) If you buy 1 share of SNOW, 1 share of RAIN and 1 share of SUN, what is the
payoff you guarantee on NYU graduation day?
(b) According to the No Arbitrage Condition, what must be the price of a $100 face
value zero-coupon bond that matures on NYU graduation day?
(c) Suppose that this zero-coupon bond is trading at $90. How would you set up a
transaction to earn a riskless arbitrage profit? Assume no trading costs.
(d) Suppose that trading zero-coupon bonds and RAIN is costless, but shorting SUN
costs $3 per $100 face value and shorting SNOW costs $1 per $100 face value.
Can you still make an arbitrage profit?
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