LM 4: Arbitrage, Replication, & Cost of Carry in Pricing Derivatives

Question 1

What is arbitrage?

Answer 1

no capital requirement of the simultaneous purchase and sale of the same or similar asset in different markets in order to profit from tiny differences in the asset’s listed price.

Question 2

What is the no arbitrage formula for forwards contracts?

Answer 2

f0 (T) = s0 (1+r) ^T

Question 3

What is replication in derivatives?

Answer 3

replicating a position using a different derivative

Question 4

What is the forward price formula if there are carry costs and benefits that are monetary?

Answer 4

f0 (T) = [ s0 + PV 0 (C) - PV 0 (I)] * (1+r) ^T

PV 0 (C) = other costs of ownership
PV 0 (I) benefits of ownership

Question 5

What is the forward price formula if there are carry costs and benefits that are continous?

Answer 5

F0 (T) = s0 e^(r+c-i)*T

r = continuous risk free rate
c = continuous cost of ownership
i = continuous benefit of ownership

Question 6

What is the spot rate formula for currency forwards?

Answer 6

price = #number of units of foreign currency / 1 unit of domestic currency

eg. USD / EUR spot rate = 1.20
price = 1.20 USD = 1 EUR

Question 7

What is the forward price formula for currency that are continuous?

Answer 7

f0 f/d (t) = s0 f/d * e ^ ((rf- rd)* (t))

s0 f/d = spot rate of currency f/d
rf = risk fee rate of foreign currency
rd = risk free rate of domestic currency
t = time out of year

Question 8

What is the principal behind derivative contracts?

Answer 8

identical assets should not trade at different prices. other wise opportunity for arbitrage.