Recent Questions - Quantitative Finance Stack Exchange

I'm curious about an exercise found in Optimization Methods in Finance . Exercise 8.2 (pg 143) explores a variant of the more commonly used form of MVO. When I refer to the more common variant I'm talking about: $$ \begin{aligned} \operatorname{max}_x \mu^Tx - \frac{\delta}{2}x^T\Sigma x & \\ Ax &= b \\ Cx &\ge d \end{aligned} $$ The variant that directly uses standard deviation by taking the squ…

I'm implementing the solution with drift from "Dealing with the inventory risk" from Gueant, Lehalle and Tapia. I'm using the link https://arxiv.org/pdf/1105.3115.pdf as reference. I can reproduce the standard solution with no issues, and then reproduce the surfaces in the paper. I'm trying now to implement the solution with drift, which is very similar to the standard solution, with a new compon…

In Mandelbrot(1968)'s paper, the fractional brownian motion, denoted by $B_{H}(t,\omega)$,(t>0) is defined by $$B_{H}(0,\omega)=b_{0}$$ $$B_{H}(t,\omega)-B_{H}(0,\omega)=\frac{1}{\Gamma(H+\frac{1}{2})}\{\int^{0}_{-\infty}[(t-s)^{H-1/2}-(-s)^{H-1/2}]dB(s,\omega)+\int^{t}_{0}(t-s)^{H-1/2}dB(s,\omega)\}$$ I have difficulty understanding fractional brownian motion by self study.Is there an intuitive…

Apologies for the rather broad question! Essentially, I wanted to ask how to build an FX forward curve from scratch. I have some basic understanding of interest rates and discounting but I am lacking the theoretical and practical knowledge to figure out how it fits together to result in an EUR/USD SP to 2Y curve, for example. How roles do instruments like IMM, OIS, etc play in it? Any links to/na…

Are there any applications of abstract algebra (group theory, rings, fields etc.) in any branch of either economics or finance?

Let's say you decide to buy a 2Y10Y ATM swaption straddle (i.e. buy 10 million ATM payer swaption and buy 10 million ATM receiver swaption). In order to delta hedge, I believe you would short the 2Y10Y forward swap. My questions are: How exactly does this delta hedging work? When do you profit from it (is it when there is a big move in realized volatility in the underlying forward swap)? What nee…

I have a payoff structure but I do not know the price of the bond. The bond is municipal. What discount rates should I take for each period in order to calculate its fair price?

I am trying to map Bloomberg ticker into Reuters one. For example this one: EDZ3C 96.625 COMDT Few years ago aforementioned BBG ticker would be mapped to Reuters RIC: GE96625L3 This can be decoded as: GE : code for Globex Exchange 96625 : the strike 96.625 L : calculated based on rule: A-L (call) and M-X (put) where A, M=Jan; B, N=Feb; ….; L, X=Dec, meaning that our option has: Expiry: December T…

I'm trying to build a day weight 'aware' vol curve (simple term structure in time, but flat across a given time slice) in quantlib. I've supplied a list of dates & vols and built it with ql.blackVarianceCurve, trying different pre-defined daycount types (Actual365Fixed, Business252 etc). My aim would be initially to produce a vol curve that has constant variance per business day. So if I were t…

Would anyone know why realised MBS (esp. Bloomberg Barclays US Agency MBS index) excess returns over duration adjusted Treasury index are systematically below the average OAS spread for long holding periods, let's say for 10y, 20y or 30y? I calculated that annualised realised excess return is roughly 20bp less then average OAS over the same time horizon.

I am trying to understand how climate risk impacts the financial market and I am calculating VaR and ES. I am applying the GARCH-MIDAS model to the FTSE MIB, using the Climate Policy Uncertainty Index (CPU) by Konstantinos Gavriilidis as an explanatory variable. The problem is that within my model confidence set, the best results are given by the GARCH and GJR models, while the GARCH-MIDAS is alw…

So, I'm using MetaTrader5 to get data and form a Binary Options bot, but to backtest I've just been keeping track (within my EA code) virtual binary Up/Down orders paired with expiry and bet amount. And if it turns out to be a winner, then incrementing a counter. Then periodically displaying win rate on chart. However, to be sure I'm not deluding myself into thinking I've got a winning EA for b…

I've bought Gatheral's book on Local Volatility and I have troubles with understanding a part where he shows that local variance is a conditional expectation of instantaneous variance. Why in the second equation from the bottom he just skips the term $\theta (S_T-K)dS_T$? He says that it's because $F_{t,T}$ is a martingale. I see that $F_{t,T}$ is a martingale, but don't know how this helps. Also…

This is a really simple question but I can’t figure it out. I was given this definition for trades in an order book. “A bid and an offer whose prices are the same or cross will pair, resulting in a trade. We consider bid and offer prices to cross when the bid price is higher than the offer price; in those cases, a trade will occur at the price of the older order” I’m a little bit confused about t…

A Wiener process has infinitely many states of the world at any time step. Does that not mean that there are infinitely many EMM's for any model that uses the Wiener process? But then if there is only one EMM for this model, how is it possible that the Esscher transform can be exactly the right transform, out of all possible transforms, to get the exact Black-scholes pricing formula?

How to understand the trade price and volume exists when ask price and volume are 0 but bid ones exist? I can't understand what happens under such condition? And also why sometimes bid price is higher than ask price? Thanks

Why would a bonds discount margin widen but its price increase? Shouldn't the price be falling when margins are widening? Looking at the bond pricing formula, if the price is higher doesn't the rate of return have to be lower? What am I missing?

I am genuinely interested in understanding a little more about the risk aggregation approaches that are out there. I have been recently working on building an operational risk model under Basel 3.1, where the following approach applies. Risks are being modelled via LogN distributions (with the option to use Weibull or Pareto). Given there is no data history, an optimistic and a pessimistic loss i…

I am working on vol surface modeling for cryptocurrencies and generally find that SABR calibrates to the vol surface on ETH better. I know that eSSVI ensures arbitrage free surfaces and therefore that we sacrifice a bit of goodness of fit for it, while SABR isn't guaranteed to be arbitrage free when interpolated, but even by adding safeguards and penalties to SABR to push the general surface towa…

I'm new in quant math, I'm self-studying it. I have two question in exp. daily range topic. How can we make the possibly most accurate estimation for expected daily ranges? My idea was to take data from yahoo finance, calculate realized vol using garman-klass-yang-zhang formula, then use a model (dunno which one) to calculate an expected trailing seven days avg historical vol for SPX. After that …