LM 10: Valuing a Derivative Using a One-Period Binomial Model

Question 1

What is the hedging ratio formula and use?

Answer 1

protect the downside risk or upside risk

hedging ration (H) = (cu1 -cd1)/ (su1 - sd1)

Question 2

Value or effectiveness of hedge or value of portfolio formula?

Answer 2

vu 1 = hedging ratio * su1 - cu1 = vd 1 = hedging ratio * sd1 - cd1

Question 3

What is the call option value formula?

Answer 3

c0 = hedging ration * s0 - (v1/1+r)

Question 4

What is the formula for binomial valuation for a call up at time 1 and call down at time 1?

Answer 4

cu1 = Max (0, su1, -X)
cs1 = Max (0, sd1, -X)

Question 5

What is the formula for stock increase and decrease of a binomial model?

Answer 5

sU1 = (1+ increase return%) * spot price
sD1 = (1+ decrease return%) * spot price

sU1 = stock increase value at time 1
sD1 = stock decrease value at time 0

Question 6

What is the risk neutrality probability formula of an upward movement?

Answer 6

pie = (1 + r) -Rd / (Ru -Rd)

r = risk free rate
Rd = return decrease %
Ru = return increase %

Question 7

What is the risk neutrality formula of a downward movement?

Answer 7

1 - pieU

pie U= risk neutrality of updward movement

Question 8

What is risk neutral formula for a call option vs a put option?

Answer 8

c0 = ((pie) * cU1) + ((1-pie) cD1) / ((1 + r)^t)

p0 = ((pie) * pU1) + ((1-pie) pD1) / ((1 + r)^t)

pie = risk neutrality of upward movement
cU1 = call option upward return at time 1
cD1 = call option downward return at time 1
pU1 = put option upward return at time 1
pD1 = put option downward return at time 1