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I think the yield curve is not what you need here. The idea is to have a model for the dynamics of the bond process $dB(t,T)$ (which you can compute by having dynamics for short-term interest rate $dr_t$. A common assumption is to use Black 76 model with $F = B(0,T)$ if I remember well. You will also need to know the volatility $\sigma$ of your bond prices. ...


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Very simply, Ross' framework assumes a great deal to extract the true pricing kernel. Time homogeneity, additively separable state dependent utility, (discrete time Markovian structure - though these have been relaxed.) In particular, there are two schools of criticism, one is that time homogeneity makes little sense in the real market. In fact, the Recovery ...


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I am guessing that the argument is as follows. They certainly have the same value at time t since they are both worth $S_t$ then. If they have the same value at $t$ they should have the same value at time $0.$ So if we are pricing by expectation our measure has to give the same discounted expectation price to both portfolios. So we must have $$ e^{-rT} ...


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if the pay-off is continuous, the standard approach is to use the path-wise method also known as IPA. This essentially means that you differentiate along each path. It is the limit as the bump size goes to zero of finite differencing. The main downside of this method is that the differentiation can be fiddly and slow. The Smoking adjoints paper you mention ...


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LSM is very fiddly. The most important things in my view are 1) don't believe anyone who says that the choice of basis functions doesn't matter. 2) implement an upper bounder, eg Andersen--Broadie (2003) or Joshi-Tang (2014) so you can tell if your prices are good 3) do two passes, one to build the strategy, one to price, if they give very different ...


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You can view the price of an option as the cost to dynamically replicate it. The more volatility, the more costs you will have trading the underlying to keep your delta equal to 0 (I'm assuming you sold the option, hence a negative gamma position). So, if at any spot, any date your local vol is above 0.194, rebalancing the portfolio will be constantly more ...


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There are two approaches. Price call and put options with various strikes. Plot their BS implied volatilities. Find the slope of the graph. Price a call and digital call with the requisite strike. Compute the implied volatility of the call. Use the fact that $ DC(model) = DC(BS) - skew \times callvega,$ to solve for the skew. (See eg Section 7.7 of my ...


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In three bullet points: Efficiency: the obtained prices maximize assumed utilities of different agents. In their paper "The Valuation of Option Contracts and a Test of Market Efficiency", Cohen, Black and Scholes compare the theoretical value of options to their market price. The efficiency is in this sense: can agents obtain more or less in practice than ...


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If I am not mistaken, the Feynman-Kac formula is related to the Kolmogorov's backward equation, so I would expect it to be available only for Markov processes. Diffusions are usually of Markovian type, in contrast to general Ito processes or more to say, general semimartinagales. Intuitively, the PDE/PIDE/... will describe the dynamics of ...


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Let me provide an intuitive answer that I just thought of (correct me if I am wrong). So starting with two Stochastic Differential Equations (SDE) $ \frac{dS_t}{S_t}=μdt+σdW_t$ $ \frac{dD_t}{D_t}=-rdt$ (I am assuming our risk-free rate to be constant as is done in most introductory financial math courses) Notice: $D_t = e^{-rt}$ is the solution to the ODE ...


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CRR is just a numerical approximation to Black--Scholes. Its main use is in getting American option price. There is no real difference other than slight inaccuracy when using it for Europeans. So no it wouldn't do what you ask. Your questions are philosophical. What is the purpose of the model? if you estimate the volatility from a time series then you can ...


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I guess the easiest would be to price a call option, and then use put-call parity. To price the call option you would have to do a change of numeraire. A good reference for this would probably be Brigo and Mercurio.


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There are lots of papers online and here are a few I would suggest math.umn riskworx G. Dimitroff, J. de Kock Nowak, Sibetz I you have matlab there is an step step example to calibrate SABR model. Since it uses the financial toolbox of matlab for a few functions I dont think you can replicate it in any other language. There must be C++ code available ...



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