Citi·Data Scientist·Technical Phone Screen
- Given a two-period binomial stock model with S0=100, up factor 1.25, down factor 0.8, and a 5% per-period risk-free rate, compute the risk-neutral probability and price a European call with strike 100 using backward induction.
- Using the same binomial tree, price an American put with strike 100 and identify any nodes where early exercise is optimal.
- Prove whether early exercise of an American call on a non-dividend-paying stock can ever be optimal in this binomial framework, and explain the intuition.
- Using a two-period short-rate tree with given up and down rates and risk-neutral probability of 0.5, price a zero-coupon bond maturing at t=2 with face value 100.
- Price a two-period coupon bond with face 100 and coupon 5 paid at t=1 and t=2 using the same short-rate tree, then report its yield to maturity and explain the no-arbitrage pricing principle behind your approach.
“The risk-neutral probability calculation itself is fine, just plug into the formula.”