Financial Engineering and Analytics
Price a call in a two-state tree
Can you value a call without forecasting how often the stock will rise?
Practise price a call in a two-state tree with a worked example and a short check.
In a one-step arbitrage-free tree, use a pricing weight that makes the expected stock value grow at the risk-free rate.
q = (S × R − Sd) ÷ (Su − Sd); call = (q × up payoff + (1 − q) × down payoff) ÷ R
(105 − 80) ÷ (120 − 80) = 0.625. Payoffs are $20 and $0. Discount $12.50 by 1.05 for about $11.90.
Stock is $100, up is $120, down is $80, strike is $100 and R = 1.05. q is 0.625. Call value is $12.50 ÷ 1.05 ≈ $11.90.
(105 − 80) ÷ (120 − 80) = 0.625. Payoffs are $20 and $0. Discount $12.50 by 1.05 for about $11.90.
With the same tree and zero interest, what is the call value?