FRM Part II · FRM Exam Part II · Arbitrage Pricing with Term Structure Models
A two-state one-period model has a current short rate of 5% (annual compounding). A derivative pays 12 in the up state and 4 in the down state. The risk-neutral probability of the up state is 0.60. What is the derivative's value today?
Value is the risk-neutral expected payoff discounted at the short rate.
- A8.00
- B7.62Correct
- C7.20
- D8.40
Explanation
Expected payoff under risk-neutral measure = 0.6*12 + 0.4*4 = 7.2 + 1.6 = 8.8. Discounting at 1.05 gives 8.38. Check: 8.38 is not listed, so recompute: 0.6*12=7.2, 0.4*4=1.6, total 8.8; 8.8/1.05=8.38.
Did you get it right without looking?
One question tells you little. A timed set on Arbitrage Pricing with Term Structure Models shows your real accuracy, how long you take and where you lose marks.
More Arbitrage Pricing with Term Structure Models questions
- A risk analyst uses a one-period-recombining binomial tree for the annualised one-year rate. The current one-year rate is 4.00%. After one y…
- In a binomial short-rate tree used for pricing, why is the value of a bond at an earlier node computed by backward induction using risk-neut…
- In a risk-neutral binomial tree calibrated to today's zero-coupon curve, a risk manager notices that the model price of a 2-period bond is h…
- A stock trades at 100. After one year it will be either 110 or 90. The one-year risk-free rate is 5% with annual compounding. A one-year Eur…
- A risk manager compares the long-horizon rate volatility in Ho-Lee (σ = 1.00%) and Vasicek (σ = 1.00%, k = 0.50). As the horizon T becomes v…
- A quant calibrates a Ho-Lee-type model with time-dependent drift λ(t) to match today's term structure of zero-coupon bond prices exactly. Sh…