Recent Questions - Quantitative Finance Stack Exchange

To model a structured product, I thought of using a geometric Brownian motion model, where I choose a certain mean and variance for the normal distribution to make sure that a certain percentage of paths (as a result from Monte Carlo) cross a threshold value where different conditions apply. However my question is does this violate the risk-free and arbitrage free assumption? Meaning I can no lon…

I am reading the book "Trades, Quotes and Prices" by JEAN-PHILIPPE BOUCHAUD and have stuck in the very beginning with understanding the formula of variance of MM's gain per trade (see picture). How is this formula derived since it is not like a standard variance formula with expected value and mean in it? It is also strange to me that we literally calculate variance for a single variable. Would b…

Today I have been struggling with something that someone here for sure has already encountered. I have a corporate issuer with a set of fixed coupon bonds (maturities between 1.5 to 20+ Years, luckily same coupon frequency), and I would like to estimate a Zero-Coupon Curve out of it. However, this is not like the dummy exercises at university where you always have a zero coupon bond as a starting…

Since the beginning of this year, LIBOR rates have ceased in some markets like GBP, CHF, and JPY and rates pricing has moved into the RFR space, using compounded overnight rates as the underlying for cap-/floor(lets). My questions now are concerned with the building of a vol surface based on broker quotes of normal par vols (absolute strikes, yearly expiries, backward looking with quarterly compo…

I am going through the book 'Introduction to Risk Parity and Budgeting' by Thierry Roncalli (2013). The author provides software for the various concepts illustrated in the book, but it is all done in GAUSS (see here ). It's a language I have never used and do not have access to. I was wondering if someone would know of a Matlab, Python or even R repository that 'translates' at least partially th…

I need to store OHLC data from the Forex Market. I live in the UK which is presently in British Summer Time +1. The Forex Market EST, which is normally -5 from GMT. I'm not sure how Eastern Daylight time Affects things. I want to store the data in a format that is consistent across timezones etc and also to know when the daily trading session starts and ends. This has got me totally confused: …

What’s the best way to hedge a down-and-in BTC put? I am not quite sure what the best practice here would be and would love to get some guidance. Thanks

I am trying to calculate the Total Credit Risk capital % for my learning purpose as given below. Assuming adding 1 single loan with different pds. i have noticed one point in the table and have two queries. Point 1: As PD increasing, the highly risky bands gets lower credit risk capital %. Question1: Is there any rational behind this?, why we need to keep lower capital for risky bands? Question2:…

I am currently working on the implementation of classic schemes to solve the BS PDE and it seems that I make a mistake in my code because the result looks far from the result of the BS formula. Here is the maths of the implicit scheme: Substituting $\tau = T - t$ into the Black-Scholes equation and using the chain rule, we get: $$-\frac{\partial V}{\partial \tau} + \frac{1}{2}\sigma^2S^2\frac{\pa…

Numerous sources refer to the 'funding cost' of a derivative. I'm confused as to exactly what cost is being referred to here. To illustrate my confusion, consider purchasing an uncollateralised OTC gold forward at market (with value of 0). I have not needed to fund anything. Now consider that forward going into the money with some positive PV. I still have not funded anything (and will not need t…

I was wondering if anyone is familiar with how credit default swaps can be used for corp funding and financing. I came across an old case where a bank created a funding structure for a client (asset manager). However, I'm not familiar with how this takes place. Any insight on the above would be greatly appreciated. Thank you, Faisal

I'm trying to model GARCH volatility on electricity prices. Typically the first step is to use prices to obtain log returns to make them stationary. I have encountered a small problem however: electricity prices can go negative. So returns defined as \begin{array}{cc} r_t:=\log(P_t / P_{t-1}) \end{array} will produce some undefined values. I have gotten around it by using differences \begin{array…

Consider a HJM framework $$d f(t, T) = \sigma (t, T) d W_t^T$$ which is a SDE of instantaneous forward rates on $T$ -forward measure, and let $$P (t, T) = \exp (-\int_t^T f (t, u) d u)$$ $$B (t) = \exp (\int_0^t f(u, u) d u)$$ be a $T$ -discount bond price and a continuously compounded money market account. By definition, \begin{align} P(t, T) &= \exp (-\int_t^T f(0, u) d u - \int_t^T \int_0^t \s…

I have completed finishing Class 12 (CBSE) and plan to pursue a career in quant finance. I have about 2.5–3.5 months before starting undergrad. I wanted to ask: What should I focus on during this time to build a strong foundation? Which skills (math, programming, stats, etc.) should I prioritize? Any specific resources, projects, or habits that would give me an edge early on? Thanks!

I'm trying to understand the physical meaning of cointegration vectors of log prices in the real world. For example, if I have two assets $A$ and $B$ , and Johansen test gives us a cointegration coefficient of [1 -1] for their log prices: $$log(A)-log(B)=\eta$$ When we convert this relationship back to real prices to understand its physical meaning, we have $$\frac{A}{B}=e^\eta$$ This makes sense…

In my experience trading in asian markets, I have found a few resources that conduct calculations on order books. They are able to provide the size and real time movements on specific types of orders classified based on their size. I can then see on the dashboard how much individual investors are buying, how much institutions are buying, etc. I was wondering if there are similar platforms that…

Right now, I was able to get an orderbook snapshots data for BTCUSDT in Binance. The problem with this data is that each depth level of the orderbook increases every 5 cents or so. For total of 20 depth levels, it amounts to only 1 dollar higher or lower from the mid price. Because i intend to hold the position for longer (around a few hours to a couple days), I want to see the bigger picture, i.…

I fit some algorithm predicting the distribution of stock future log returns , based on historical prices. The optimisation goal - best fit of European options premium . Done as backtesting on historical prices - start with 0 cash, and after selling millions of European Calls and Puts with various strikes, compared with actually realised outcomes from historical stock prices on expiration date - …

I downloaded adjusted closing price using quantmod for a set of securities. I want to calculate daily/weekly/monthly return for all securities. Usual dailyReturn, weeklyReturn etc not working. What do I need to do? Here is my code. tickers <- c('FB','MMM') data_env <- new.env() getSymbols(Symbols = tickers, env = data_env) tempPort <- do.call(merge, eapply(data_env, Ad)) head(tempPort ) …

Sometimes I'll see sources online say things like markets are pricing in a certain amount of bps rate cuts/hikes by the Fed or ECB (or some other central bank) for a certain monetary policy meeting date My main question is WHERE is this information found or how is it derived? I'm getting quite confused by looking at sources online The only thing I found publicly available which makes sense is the…