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Interesting Undergrad Thesis [on hold]

I'm searching for an undergrad thesis in finance. I already have some ideas, but still wanted to ask: Is there a an interesting topic that jumps to your mind, when you think about implied volatility (...
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What data sources are available online?

What sources of financial and economic data are available online? Which ones are free or cheap? What has your experience been like with these data sources?
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Interpretation of Fama French portfolio

I have two portfolios, one "bad" and the other "good". I construct the portfolios by taking the average monthly returns based on some criteria each year. In any given portfolio there could be between ...
72 views

In Joshi's Concepts and Practice in Mathematical Finance, page $110,$ he stated the Ito's Lemma: Theorem $5.1$ (Ito's Lemma) Let $X_t$ be an Ito process satisfying dX_t = \mu(X_t,t)dt + \sigma(... 1answer 132 views Mean Variance Investment problem I attach a part of a paper explaining how the weights of a market portfolio are derived. I do not understand how equation 5 has been derived and, in particular, where the zero beta portfolio's return ... 1answer 51 views Why Joshi defined option value to be discounted payoff using risk neutral expectation? Currently I am reading Mark Joshi's The Concepts and Practice of Mathematical Finance. At page 59, the author mentioned the following. Instead of requiring that every portfolio should have ... 1answer 130 views Calculate the price at time t=0 Assume the risk-free bond Bt and the stock St follow the dynamics of the Black & Scholes model (with interest rate r, stock drift \mu and volatility \sigma). Calculate the price at time t = ... 3answers 264 views Compute the price of a derivative Consider the payoff function \begin{align*} f(x)=\begin{cases} 3 & \text{if }x\leq 30, \\ 33-x & \text{if }30<x<35, \\ -2 & \text{if } x\geq35. \end{cases} \end{align*} How would I ... 1answer 78 views Is the european put option an increasing function? My question is to show that the function K \rightarrow p(T,K) is increasing. T being maturity time,K being any strike and p(T,K) is a european put option. My only approach to this question has ... 1answer 85 views Finding todays price of a derivative Today's market prices for European call options c(T;K) and put options p(T;K) with maturity T and any strike K. Let B_t = e^{rt} be the price of the risk-free bond and St the price of the stock. ... 1answer 38 views How to deal with intermittent NA values in a price series when calculating returns Let's say a have a price series for a share for the year 2000. On the 27th of July 2000, there is a missing value represented by NA. This was not a holiday or any other non trading day as other shares ... 1answer 38 views Show that \frac{\partial c(t))}{\partial \sigma^2 }>0 \text{ if and only if } S(t)<Xe^{-r(r+\frac{1}{2} \sigma^2 )(T-t)}. Statement: if c(t) is the price of the digital cash-or-nothing call option, then direct calculation (under Black-Scholes assumptions) shows that\frac{\partial c(t))}{\partial \sigma^2 }>0 ...
Currently, I am reading John Hull's Options, Futures and Other Derivatives. On page 401, the author mentions the following: Suppose that the delta of a call option on a stock is $0.6$, stock price ...