# All Questions

94 views

### Math basics of Equally-weighted Risk contributions

i'm writing my BA Thesis about "Equally-weighted Risk contributions". Can anyone recommend math books for further understanding of Risk contributions?
312 views

### Transaction Costs for Currency Pairs

I have been aggregating some tick data from Oanda's streaming API to try and get an idea of the relative cost and best time to trade different currency pairs. The idea was to plot the spread of the ...
486 views

### What is the intuition behind the fact that Modified duration = Macaulay Duration / (1+r)?

I understand the derivation of both:take dP/dR and divide by P which will give you both 1) modified duration OR 2) macaulay duration / (1+r) (notice the weighted average time built into the ...
179 views

### Does a delta hedged short option guarantee profit of extrinsic value at expiration?

If a trader shorts an option and dynamically delta hedges to ensure the delta is equal to 0 if that option expires out of the money does the trader profit that options extrinsic value at the time of ...
370 views

### Trading days or Calendar days for Compound Annual Growth Rate?

When calculating CAGR for intervals shorter than a year (or intervals that are longer than, but not integer years in length), should you use the 252 trading days or the 365.25 calendar days? The ...
103 views

### Ability of hedge funds to transform illiquid assets

In this discussion of a Citi paper, on the impact of collateral management and rising financing costs for hedge funds, there is a quote from Sandy Kaul's statement: Sandy Kaul, head of business ...
263 views

### Which is the correct definition of arbitrage?

Spin-off from here. In Tomas Bjork's Arbitrage Theory in Continuous Time (or here), $\exists$ 2 inconsistent definitions of arbitrage, which is correct? The first definition is for the single period ...
302 views

### Forward rates formulae

I am now working with forward rates and have somehow been asked to use an "intuitive" formula for forward rates. $$\frac{F(0,s,T)}{F(0,t,T)} = \frac{F(s,s,T)}{F(s,t,T)}$$ I can understand the ...
181 views

### Inconsistent Definition of Arbitrage in Bjork?

In Tomas Bjork's Arbitrage Theory in Continuous Time (or here), $\exists$ what seems to be 2 inconsistent definitions of arbitrage: The first definition is for the single period Binomial model The ...
208 views

### Getting the next price of a GBM with reversion

Here is the "twin" question of Getting the next price of a GBM (Geometric Brownian Motion) but for GBM with reversion As in that case, I'd like to write a formula for the next price, as function of: ...
360 views

### Getting the next price of a GBM (Geometric Brownian Motion)

I am writing a program that creates realizations of a GBM. Starting from an initial price, I get the following price with this formula: ...
284 views

190 views

### Counterparty risk tutorials

I want to learn about the latest methods used to measure credit risk, which I believe is same as counterparty risk. Can you please direct me some links for this. I have come across a few of them but ...
128 views

### How To Account For Inflation Over Historical Data

I believe inflation is greatly affecting my sample data, even when using percent-changes for movements. I have read this post, which recommends the formula ((Current-Base Year CPI) * Price) / ...
557 views

### Kelly Capital Growth Investment Strategy (Example in R)

In the paper Response to Paul A Samuelson letters and papers onthe Kelly Capital Growth Investment Strategy pages 5 and 6 Dr William T Ziemba, gives a praticle example on Kelly Growth. I’m trying to ...
345 views

### How Much Capital is Needed to Start an Arbitrage Strategy?

I'm trying to experiment with a simulated simple arbitrage strategy. I'm not doing this to actually invest, I'm just curious if the market is inefficient enough for this to be feasible. Every ...
200 views

### Using Fourier Transforms for stock option pricing with stochastic interest rates

Can Fourier transforms be used to derive the joint probability density function of stochastic interest rates and stock price Brownian motions of call options under stochastic interest rates? So lets ...
441 views

### Implementing A 50/50 Prediction Model Strategy

Reworded the question for clarity (see edits for original post): How can one knowingly foresee where a 50/50 prediction model will be profitable? For previous posts: I understand that if I have a ...
97 views

### Joint distribution from expectations

Given two random variables $X$ and $Y$ and let $K$ be a constant value. Assume the expectation $\mathbb{E}[X(Y-K)^{+}]$ is given for all possible values of $K\geq 0$. Is there a way to derive the ...
3k views

### How to distinguish total return and absolute return funds in the KIID

I hope this question is on-topic. It is not relally a quant question but it is a question that quants in risk management in asset management firms have to answer: In the KIID (key investor ...
279 views

### Plot Evolution of portfolio weights over time in R [closed]

Is there any function for plotting the evolution of portfolio weights over time in r?. I have a matrix of portfolio weights from an equal weighting strategy at rebalancing times and want to plot ...
409 views

### What are the unfair order execution/routing advantages HFT firms apparently have?

I originally thought that you have an orderbook per stock and orders would be filled on the time at which they arrive. Arrive first and you get the best price and the qty in the orderbook is reduced ...
184 views

### For Probability of Default in retail credit what is more popular logistic regression or GLM with Poisson distribution and why?

Trying to understand which regression model is more popular in retail credit card industry Logistic regression or GLM with Poisson distribution and why?
133 views

### What is the correlation of and Index's dividend yield relative to its constituents?

I would like to know if the dividend yield of and index is correlated with the dividend yields of it's components separately? The purpose of this, is to use the dividend yield of the index as a proxy ...
132 views

### Combining BHHH and Levenberg Marquardt

I already asked a question related to this here: How to apply Levenberg Marquardt to Max Likelihood Estimation I know understand how Levenberg Marquardt (LM) can be applied to the objective ...
128 views

### Future spot price versus current forward price

Which are the two conditions necessary to claim that the future spot price will have as many chances to be above or below the current forward price?
38 views

### Common point between IR and Vol option pricing models?

What is the common point between pricing models on options on Interest Rates and options on Volatility?
95 views

### How do I prove that $\lim_{K\searrow0}\frac{P(K,T)}{K} = \mathbb P(S_T=0)$?

I am trying to prove that $$\lim_{K\searrow0}\frac{P(K,T)}{K} = \mathbb P(S_T=0)$$ where $P(K,T)$ denotes the put option price with maturity $T$ and strike $K$ for some stock $S$. Assuming interest ...
307 views

### How to apply Levenberg Marquardt to Max Likelihood Estimation

In this paper on p315: http://www.ssc.upenn.edu/~fdiebold/papers/paper55/DRAfinal.pdf They explain that they use Levenberg Marquardt (LM) (along with BHHH) to maximize the likelihood. However as I ...
225 views

### what is the actual point of vega on real option data

For a call option, we know that the vega is the derivative of the price wrt to the volatility. However the volatility, in that context, actually refers to the implied volatility of the specific call ...
176 views

### economic facts that causes the financial time series to be heavy tailed

When reading a tutorail on extreme value theory, I once meet the following claim ...
2k views

### Regime-Switching Model for detecting market shifts

I'm always wondering whether anyone has utilized regime-switching models successfully in forecasting or trading. Academia has long discussed this topic in-depth, such as using Regime Switching ...
685 views

### How to combine trading signals to achieve higher capital efficiency?

I trade use a completely automated approach where all signals are generated by proprietary trading strategies. However, recently I encountered an challenging problem: Imagine we have 3 Strategies ...
1k views

### Self-financing and Black-Scholes-Merton formula

Self-financing is an important concept in financial product replicating, normally used in pricing. I read about several ways to derive Black-Scholes-Merton (BSM) formula. Seems some approaches ...
753 views

### Does pricing quant still have bright future?

With regulators tightening the tether, tradings are shrinking and exotic products are fading out, or as my quant friends told me so. By the lag of education to the market, more MFE graduates are ...
157 views

### In a Black-Scholes world, why must volatility be strictly increasing in time-to-expiration?

This question is from Rebonato's Volatility and Correlation 2nd Edition. Rebonato states that if $\sigma_T^2T$ is not strictly increasing, it would be simple to set up an arbitrage. Unfortunately ...
437 views

### Arbitragefree Pricing: Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if and only if there exists an equivalent martingale measure Q, under which the discounted asset price ...
138 views

### How current prices is formulated in markets?

I can't understand how immediate prices are formulated in stock & currency (Forex) markets. I have been informed that every tick means one new deal that closed in current price, but this can't be ...
968 views

### Do hedge fund trading desks use portfolio optimization?

I tend to think that hedge funds that actively trade (and most of the ones I have seen trade very actively), don't use optimization methods like MVO or ...
63 views

### European Option Technical Exercise

I like to ask a practical question regarding the exercise of European Options: As we know, one may exercise a European option only at maturity $T$. But for example, if the option can be exercised ...
797 views

### Pricing an interest rate swap using Eurodollar futures

I see this posted but no answer given. I think it would be a good idea if we have a question on here to illustrate an example of how to price an interest rate swap. So far, I understand that that for ...
2k views

### Quantitative Math required for Market-making?

I understand there is an awful lot of Quantitative Math required for statistical arbitrage/algorithmic trading. However, would someone "in the know" be able to tell me whether there is less ...
Question about forward vs spot simply-compounded spot interest rate.Some definitions $P(a,b)$ a zero coupond price at time $a$ and maturity $b$ $L(a,b)$ simply compounded spot interest rate set at ...