# All Questions

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### Transition densities in the Heston model

Knowing the Characteristic function $\Phi_{T,t} = \mathbb{E} [ e^{i u S_T} | S_t, V_t]$ (or equivalently, the Laplace transform) of an affine process, it's possible to know the distribution of the ...
1k views

### Explanation or implementation of Ledoit-Wolf estimator (without math packages)

I have calculated weights of selected assets in a market-neutral portfolio (presumably with min variance) using PCA and simple data covariance matrix. The question is : It is obvious that Cov Matrix ...
257 views

### Applications of distance correlation

This question mentions distance correlation. Where has this concept been applied to financial data and provided new insight? Do you know any examples or references?
209 views

### Feller Condition (Cox-Ingersoll-Ross) source

For the Cox-Ingersoll-Ross model $$\text{d}r_t = a(b-r_t)\text{d}t+\sigma\sqrt{r_t}\text{d}W_t$$ the condition (referred to as "Feller condition") $$2ab\geq\sigma^2$$ ensures that the solution is ...
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### Quantitative and regulatory aspects of portfolio integration in IRB credit portfolios

Say bank A buys a credit portfolio "B" (e.g. corporate loans or retail mortgage, ...) from bank B. Bank A fulfills the the requirements of CRR (capital requirement regulation) for its existing ...
108 views

### Estimation of right truncated poisson process

I have following problem: Imagine I generate large number of homogenous poisson process sample paths (by sample path I mean a sequence of arrival times $\tau_i$ all with the same intensity. However ...
107 views

### Mathematical Representation of Adaptive Markets Hypothesis

It has been about 13 years since Andrew Lo published The Adaptive Markets Hypothesis. It provides valid criticism to Efficient Markets Hypothesis and brings lots of innovation over it. Unfortunately, ...
354 views

### How do you actually solve a stochastic HJB equation in practice?

I've read a number of recent papers on market making. Nearly all of the more recent papers focus on defining the problem in terms of a state and action space, deriving the relevant HJB equations and ...
295 views

### What are the essential characteristics of asset prices?

I think the question has already been asked about stylized facts of asset returns; this question regards the essential characteristics and normative assumptions used to evaluate asset prices. I.e., ...
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### Stress testing covariance

Going one level beyond stressed scenarios, to parameters e.g. for a VaR measure: what are the most common approaches for stressing a covariance/correlation matrix, especially taking portfolio exposure ...
1k views

### Asymmetric Volatility Modeling (Interpretation)

I am currently writing a paper on asymmetric volatility modeling of brent, gold, silver, wheat, soybean and corn from 1986-2012 and divided them into 4 sub-sample periods (i.e. 1986-1991, 1991-1997, ...
199 views

### Arbitrage free price of a derivative when the price is collected over the lifetime of the derivative

Let $X_t$ be an american style financial derivative with random exercise time $T$ where $t$ and $T$ belongs to some finite set $A$. Buying this derivative requires the buyer to pay $p_t$ up to time $T$...
974 views

### Is there a standard method of scaling alpha forecasts to t-cost estimates?

Given a set of monthly alpha forecasts (i.e. standardized z-scores from a multi-factor return model) and a non-linear market impact model (or more specifically, its piecewise-linear approximation), is ...
217 views

### How companies choose earnings release dates, & effect on Implied Volatility

A company's earnings release date significantly affects weekly or monthly option prices/implied volatility. For companies that typically release earnings on the cusp of monthly options expiration, ...
420 views

### Taking into account the correlation in Barrier options on a Basket

In a Barrier option (where the contract cancels when the underlying hits the barrier) I succesfully found the way to compute the probability of a single underlying touching the barrier (with constant ...
263 views

### Significance testing of average returns from Sharpe ratio

I'm aware that one way to do significance testing on a strategy is based on the sampling distribution of its Sharpe (see, e.g., Lo, 2002 and Opdyke, 2008). However, it appears to me that there's ...
2k views

### Commerical delayed stock quote feed that is redistributable?

I'm looking for a commercial delayed quote feed that will allow us to distribute delayed US stock market quotes to the public (ie. that will allow us to display US delayed quotes on the Internet). We ...
117 views

### First principles in Finance

Every so often I hear people referring to the term "first principles". It seems to me that this term does not necessarily have a universally accepted connotation in Finance. Here is the general ...
61 views

### How to explain the asymmetry of vanilla Volga?

I've plotted the charts of Volga of Vanilla Call/Put using finite difference method, and found they are the same, and an asymmetrical shape of observed for both. Any intuitive way to explain the ...
129 views

### monte carlo simulation

I'm a graduate student working on a real options research problem suggested to me by my advisor. I'm not looking for a solution, but I'd like to know about the feasibility of numerically solving the ...
111 views

### Discrete vs continuous

When pricing equity futures with the cost of carry model; When do you use continuous compounding and when do you just use discrete compounding? And why
80 views

### Distribution of portfolio values with constant spending rate

If your portfolio is invested in an asset that follows a geometric Brownian motion, and you withdraw a constant dollar amount at the beginning of each year, is there an approximate analytical ...
98 views

### Implied Funding/Borrow Costs in Short-Dated ETF Option Prices

I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
142 views

### SABR Question: Why does the market take the beta parameter as a constant?

SABR Question Why does the market take the $\beta$ parameter as a "constant"? I see most brokers quoting SABR parameters nowadays. I've seen many banks use $\beta$=0.5 as a rule. I've seen quants ...
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### Expected turnover from rebalancing

If you have a target weights for N assets with monthly returns that are drawn from a multivariate normal distribution with known means and covariances, is there an exact or approximate analytical ...
131 views

### Merton's portfolio problem with constraints

Suppose the investor can invest in a Black-Scholes market with one risky asset $S$ with drift $\alpha$ and volatility $\sigma$ and a riskless asset $B$ with a riskless rate of return $r$, and the ...
173 views

### No-arbitrage in term-structure models

I am a bit confused about what the implication of "no-arbitrage" in popular term struchture models (such as affine term struchtre models or HJM models) are? Is it solely a restriction on the cross-...
405 views

### Risk management tools for long term Gamma/Vega sellers subject to margin calls

TL;DR: if you're a retail investor and you systematically sell long-term vertical spreads while staying Delta-neutral, your main risk comes from Vega and the Gamma of opening gaps that can throw you ...
182 views

### Implementing Hanson`s LMSR with Limit Orderbooks

I am trying to integrate Hanson's LMSR (see (see logarithmic market scoring rule)into an order-book with traditional bid/ask-limit orders (in KDB+/Q). The following functions define the basic LMSR ...
46 views

### Martingale property of inhomogenous poisson process

I have found this martingale property for an inhomogenous poisson process with intensity $\lambda(s)$ which I don't know how to prove. The text itself advises: "proceed using Monotone class theorem". ...
421 views

### Gyöngy Theorem Proof

Can you please point me to a publicly available text that discusses the proof for the Gyöngy Theorem? Gyöngy, I. (1986), “Mimicking the One-Dimensional Marginal Distributions of Processes Having an ...
235 views

### Dupire's calibration

I'm trying to implement a method for calibrating the local volatility model (Dupire's one). I'm working on the paper from Andreasen and Huge : Volatility interpolation (SSRN). Is this considered to be ...
228 views

### Bayesian strategy selection

I have N strategies/signals that I would like to allocate to. I want to estimate an estimate of future performance based off of recent realized performance (momentum of strategies per se - e.g. ...
112 views

### Pricing and hedging of vanilla options based on non-tradable underlying

Consider a non-tradable stock index $S$ which satisfies: $dS_t=\mu S_tdt+\sigma S_tdW_t$ and a risk-free asset $B$. I want to price an European Call option with the payoff $C_T=max(S_T-K,0)$. The ...
Consider an arbitrage-free and complete financial market with underlying filtered probability space $(\Omega,\mathcal{F},\{\mathcal{F}_{t}\}_{t\,\in\,[0,T]},\mathbb{Q})$, where $T\in(0,\infty)$ is ...
Hi Quantitative Finance Stack Exchange, I'm looking for an opinion on a simple question. Suppose I use a Garch(1,1) model to make a volatility forecast. At time $t$, I have realized volatility \$\...