Tagged Questions

Questions about models for the valuation of option contracts.

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A question on option pricing [closed]

Calculate the value of 9-month American call option to buy 1 million units of a foreign currency using a three-step binomial tree. The current exchange rate is 0.79 and the strike price is 0.80 (both ...
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Black-Scholes under stochastic interest rates

I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are ...
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Consider the stock price process satisfies the following SDE: $dS_t=\mu_t S_tdt + \sigma S_t dW_t , S_0=s$ and the appreciation rate process $\mu_t$ satisfies the following SDE: $d\mu_t=(a-\mu_t)... 2answers 180 views How to calculate Implied Volatility for out-of-the-money options? I'm trying to calculate the implied volatility for out-of-the-money options, and to a lesser extent, in-the-money options. Most of the literature estimations I could find for implied volatility were ... 1answer 74 views Arbitrage opportunity in discrete time Say we have the following binary option$B$on asset$S$with strike K and expiration time T, assume also that the following relation holds at time$0$:$B > N*C(K,T)-N*C(K+1/N,T)$Where$N$is ... 0answers 47 views Capital increase: which stock price to use as input to Black-Scholes formula? For an exercise we have to calculate the theoretical value of a scrip / preferential right on its issue day (23 April) in the context of a capital increase. The scrips are issued on 23 April. The ... 2answers 80 views Counting random paths Assume the path of a certain stock can be modeled using a binomial tree. The initial price of the stock at time$t=0$is 1024. The upstage factor of the stock price is$x=1.25$and downstage factor of ... 1answer 57 views Option pricing: Risk neutral probability calculation Let$u=1.3d=0.9r=.05S(0)=50, X = \text{strike} = 60$. Assume binomial model Why isn't the risk neutral probability found by solving the following for$p$:$$E[S(T)]=p65+(1-p)45=S(0)(1+r)^T=... 5answers 391 views Estimate probability of limit order execution over a large time frame I have a negligible amount of money (\$5000) that I would like to invest in a stock. I would like to buy the stock at some point in the next year, and get the lowest possible price. I would like to ...
Prove that the price of the European put option is a convex function of the strike price in one-step binomial model. In other words, if $P_E(X)$ is the price of the European put option in one-step ...