Reference no: EM132329719

Problem -

(i) Consider a non-dividend paying stock with current price $100 and return volatility σ = 18.23 [% p.a.]. Construct the one-period (T=1) binominal tree. The risk-free one-period rate y(0;1) is 3%. Value a European Call with exercise price E= $110 and maturity T = 1 by

• the replication principle,
• the hedging principle, and
• by means of risk-neutral probabilities

(ii) Consider the stock price as defined in (i). Value a European Putn with exercise price E=110 using all three valuation methods of (i).

(iii) Extend the one-period binominal tree of (i) to a two period (T=2) recombining tree. Assume y(0;2) = 3%. Value two year European and American Calls with exercise price E =110.

(iv) Value two-year European and American Puts using the tree constructed in sub-problem (iii).

(v) Assume the stock pays in t=1 a 5% dividend on the stock price S₁^cum. Solve (iii) and (iv) for this case of a dividend paying stock. Compare the results of the European and American Call resp. and try to explain the differences.

(vi) Solve (v) for the European and American Call if a dividend of 15% on the cum-stock price is paid.