Assume X(t) = 0 for t < 0, and start with Y(0) = p_0 X(0) which is trivial to invert. Then just work sequentially through Y(1) , Y(2), etc. Thanks, Alan. Interesting idea leading to simplifications but I don’t think I can assume that. T=0 is today and I have a sequence of well-defined, non-zero X(t...

I have a dependent variable Y(t) which depends on an independent variable X(t) in the following way: Y(t) = p_0*X(t)+p_1*X(t-1)+p_2*X(t-2)+...+p_n*X(t-n) where p_i=cosnt, 0<=p_i<=1 and sum(p_0+...+p_n)=1. So, given a history of n consecutive variables X(t), I can always calculate the "current&q...

The MBA (mortgage bankers association) provides a monthly report of actual and forecasted US residential mortgage originations (purchase and refi number of loans 000's): https://www.mba.org/docs/default-source/research-and-forecasts/forecasts/mortgage-finance-forecast-apr-2022.pdf?sfvrsn=983665d9_2 ...

Hi - Suppose someone tossed 100 coins and then covered them up. They ask you how many heads you expect, and absent other info you say 50. Suppose now that this person uncovers 20 of the 100 coins and shows you 20 heads. Note that they don't randomly uncover 20 coins which happen to be all heads - th...

Thank you! Both your responses make sense - you can’t improve the inequality in general but certainly there are ways to optimize this for specific distributions given the information we have.

Hi all - I have two independent (but not necessarily identically distributed) random variables: 𝑋>0,𝑌>0. All of their moments are known but we don't know the distributions. Can we find an upper bound for 𝐸[𝑚𝑖𝑛(𝑋,𝑌)] that is better than 𝑚𝑖𝑛(𝐸[𝑋],𝐸[𝑌]) with the information given without knowing the di...

Not sure I follow entirely, Alan - if we are looking at a lookback option for instance with payoff Max[F(0),...,F(T)]-F(T), then the derivative depends on the joint distribution of the maximum and the forward price. Is it obvious that the derivative price depends on vol*sqrt(T) (which is the case si...

Agreed and thanks for pointing that out, I had overlooked the discounting so that clearly doesn't hold in the examples you provided or Black-Scholes where you have the K*exp(-r*T) term. But if the payoff doesn't depend on the money market account and can be expressed only in terms of the stochastic ...

Hi, Suppose that a stock price follows standard GBM process with constant risk-free rate and constant vol. Suppose we also have some derivative with unknown payoff P(.) at expiration T which depends in some general way on the stock price process (it could be just ending stock price or path dependent...

Thanks for your reply, bearish! Point well taken about not relying on obscure papers on the internet. However I did look at a few papers before posting the question and they all suggested that formula, plus I know Margrabe’s formula of which this is a special case where one of the asset is a stock f...

Hi all, I was looking at option prices which incorporate stochastic interest rates, as in the following paper - formulas 4 and 5 on p.9: http://www3.nccu.edu.tw/~liaosl/Publication/28.pdf So looking at the adjusted volatility term, the higher the correlation between stock returns and bond returns (i...

Let A = Integral [0...inf] f(t)dt, A>0. Suppose I have the following integral: B=Integral [0...inf] f(t)*exp(-kt)dt where k>0 is a constant. Is it possible to have a bound for B (upper or lower) in terms of A and k? I tried Cauchy-Schwarz but that only gets you to integral of f(t)^2 and not sure if ...

Thank you Paul and Alan, very helpful. @Paul, it wasn't clear to me what you meant all along by saying "plot the value". I thought you were suggesting looking at the values at various nodes of the binomial relative to the exercise payoff at that node. Did you mean plotting the euro-style c...

stilyo, sketch the value of the euro version before expiration, it's v easy. The answer to your question will be obvious. After that we can talk about solutions with and without dividends. But at all times ignore the noise from list1. He means well but doesn't know what he is talking about. Thanks,...

Please define the contract unambiguously for us. Stock price is S(0), strike is K, threshold is L where S(0)<K<L. The option can be exercised at any point between now and maturity T at the choice of the option holder where the payoff is Max(S(t)-K,0). If at any point the stock price crosses the thr...