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中文题目In a one-period binomial model, S0=100, Su=120, Sd=90, and the simple risk-free rate is 0. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.
打开 →In a one-period binomial model, S0=50, Su=65, Sd=45, and the simple risk-free rate is 0.05. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.
打开 →In a one-period binomial model the stock has S0=100 and goes to Su=130 or Sd=90, with risk-free rate 0. A call struck at K=100 trades at price 12. Back out the implied risk-neutral probability of the up state from this option quote.
打开 →A one-step binomial tree has up factor u=1.15, down factor d=0.88, continuously compounded rate r=0.05, and Δt=0.5. Compute the risk-neutral probability of an up move.
打开 →On the same binomial tree, an analyst estimates a real-world up probability of 0.65 from historical data, while the risk-neutral up probability is 0.52. Which probability should be used to price a derivative by discounted expectation, and what governs the gap between the two?
打开 →Why would it be a category error to judge a forecasting model's backtest solely against risk-neutral densities implied by option prices?
打开 →Why should the binomial-tree risk-neutral probability not be interpreted as your actual forecast of an up move?
打开 →A one-step binomial model gives next-step option payoffs 1 in the up state and 9 in the down state, with risk-neutral up probability 0.5 and interest rate 0.00% for the step. The option's immediate exercise value today is 4.5. What are the European and American values today?
打开 →In a one-step risk-neutral model, the terminal payoffs are 20 and 2, the up probability is 0.55, the step rate is 2.00%, and immediate exercise today is worth 10.2. What is the American value today, and what is its premium over the matching European?
打开 →A one-step binomial model gives next-step option payoffs 0 in the up state and 14 in the down state, with risk-neutral up probability 0.45 and interest rate 5.00% for the step. The option's immediate exercise value today is 7. What are the European and American values today?
打开 →A stock has spot 100, strike 100, rate 0.03, dividend yield 0.01, volatility 0.2, and maturity 1. Under Black-Scholes, what are the forward price F_0,T and the risk-neutral probability that the call finishes in the money?
打开 →A stock has spot 95, strike 100, rate 0.04, dividend yield 0.02, volatility 0.25, and maturity 0.5. Under Black-Scholes, what are the forward price F_0,T and the risk-neutral probability that the call finishes in the money?
打开 →A stock has spot 120, strike 110, rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5. Under Black-Scholes, what are the forward price F_0,T and the risk-neutral probability that the call finishes in the money?
打开 →A desk uses the simplified risk-neutral drift relation mu_Q = r - lambda*kappa for a jump-diffusion. If r = 3.00%, lambda = 1.2, and mu_Q = 0.60%, what jump compensator kappa is implied?
打开 →A risk-neutral jump-diffusion uses mu_Q = r - lambda*kappa. If r = 4.00%, lambda = 0.8, and kappa = 1.00%, what is mu_Q?
打开 →A desk uses the simplified risk-neutral drift relation mu_Q = r - lambda*kappa for a jump-diffusion. If r = 1.50%, lambda = 2, and mu_Q = -0.30%, what jump compensator kappa is implied?
打开 →A stock has spot 90 and 1-year discounted risk-neutral expectation E[e^{-rT}S_T] = 88.218. What continuous dividend yield q is implied?
打开 →Under risk-neutral pricing, spot is 120, risk-free rate is 4%, dividend yield is 1.5%, and maturity is 2 years. What is E[S_T]?
打开 →In a one-step risk-neutral model, the terminal payoffs are 0 and 16, the up probability is 0.5, the step rate is 4.00%, and immediate exercise today is worth 9. What is the American value today, and what is its premium over the matching European?
打开 →A one-step binomial tree has spot=100, strike=100, u=1.1, d=0.9, rate r=0.05, continuous dividend yield δ=0.02, Δt=1. Using the dividend-adjusted risk-neutral probability, price the European call.
打开 →A one-step trinomial tree uses spot 100, strike 102, multipliers u=1.12, m=1, d=0.9, risk-neutral probabilities (0.25, 0.5, 0.25), rate 0.03, and Δt=1. What is the European call price?
打开 →A one-step trinomial tree uses spot 80, strike 75, multipliers u=1.1, m=1, d=0.92, risk-neutral probabilities (0.3, 0.45, 0.25), rate 0.04, and Δt=0.5. What is the European call price?
打开 →In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 84.13% and you may use the standard-normal identity N(--1) = 0.8413. What d2 is implied?
打开 →In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 15.87% and you may use the standard-normal identity N(-1) = 0.1587. What d2 is implied?
打开 →In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 30.85% and you may use the standard-normal identity N(-0.5) = 0.3085. What d2 is implied?
打开 →In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 69.15% and you may use the standard-normal identity N(--0.5) = 0.6915. What d2 is implied?
打开 →The stock is 100 today and ends at 120, 100, or 80 next period. Consider a claim paying 20, 10, and 0 in those three states. Can it be replicated exactly using only the stock and cash? If yes, give the hedge. If not, identify the replication obstruction.
打开 →Price an American put with strike 100 on a two-step tree: spot=100, u=1.2, d=0.8, r=0.03, Δt=1. Give the time-0 value and state whether early exercise occurs at the first down node.
打开 →In a one-step binomial tree, the stock is 80 today and moves to 88 or 64 next period. The strike is 85 and the one-period risk-free rate is 0.1. What is the American put value today?
打开 →A stock has three future states with prices 120, 100, and 80; the risk-free rate is 0. Calls struck at 80 trade at 28 and calls struck at 100 trade at 8. Using the digital/butterfly decomposition, find the Arrow-Debreu price of the single highest state (the state where the stock
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