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108 views

Including a score or a rank in portfolio-optimization

I have gathered a lot of experience using min-var optimization of the form $$w' \Sigma w \rightarrow Min,$$ where $w$ are the weights of the assets and $\Sigma$ is the covariance matrix. Of course ...
120 views

Black Scholes: two assets, same $W$-process

Consider a Black Scholes model with two risky assets that are driven by the same $W$-process, and then 1 risk-free asset. When is this model arbitrage-free and complete? We have only 1 driving ...
2k views

Implied Volatility of stock on Think or Swim

Think or swim has this thing where they have do a implied volatility of a stock. I have chatted with the TOS people but they aren't terribly helpful. Regardless they did send me two images of what ...
166 views

Why does portfolio optimization require a positive-definite covariance matrix?

Why does the portfolio optimization mean-variance model require the covariance matrix to be positive-definite? Does this requirement have to do with the need to be able to invert the matrix during ...
204 views

Why worry about fat tails, if you can use stoploss?

Sorry this might sound a silly question, but -humbly- I don't understand why models assume that returns range from [-∞,+∞] instead of [-stoplimit, +takeprofit]. A common objection to most models is "...
2k views

Please Explain the Debt to China [closed]

Can someone please explain to me how we are in debt with China? Every weblog, article, journal I read have people in the comments going insane about how we "owe China monies" and "China owns the US" ...
1k views

How to get/estimate ask/bid price for backtesting for OHLC data? [closed]

As you know, most of the EOD data available have only OHLC price. I used to do back-testing using the Close price as both bid and ask. however, in real world, the bid and ask spread is huge and the ...
111 views

Inverted Yield Curve [closed]

In an article of FT today, Matthew Klein writes, "The yield curve represents the cost of borrowing over different amounts of time. Lenders generally prefer getting their money back sooner rather than ...
135 views

What is the effect of increasing volume depth to stock volatility? [closed]

Say, an investment bank want to hedge its Long Gamma position on its Long Call option by placing limit orders in the exchange. Limit orders result in increasing volume depth. Empirically, what is the ...
1k views

How is the Wiener integral $\int{WdW}$ calculated?

I want to calculate $\int ^t _0 W_tdW_t$ I know that the reasoning is the following: Let $x(t)=W(t)$ with $a=0$ and $b=1$ in the definition of an Ito Process, and $f(t,x)=x^2$. Then, applying Ito'...
914 views

Target daily ROI for a market-making algorithm

I'm designing a market-making algorithm, I was wondering what a decent ROI / day would be to aim for in such a system?
79 views

European call options and strikes [closed]

We consider 2 European call options with the same underlying asset, the same maturity date $T$ and with 2 different strikes $K_1$ and $K_2$ such that $K_1\leq K_2$. We denote $C^1_{0}$ and $C^{2}_{0}$ ...
485 views

Suggestions for a Master thesis in option pricing models

I am willing to do my Master Thesis about option pricing. Do you have any suggestions? I would like it to be something simple, like comparing methods, e.g. compare ARCH and GARCH approaches for ...
318 views

Detect trend of an index

My question is about determining the trend and it can break down to 3 parts. To clarify, a trend in my point of view, and in simple form, is the last close at time t relative to its time reference, i....
69 views

implied volatility indice and implied volatility [closed]

Can anybody explain to me Why should we calculate implied volatility if there is already an implied volatility index where implied volatility is already calculated??? I can't understand the difference
220 views

Does the Ito correction term in GBM result in 'real money', or is it illusory?

There are two ways to think about investment returns and randomness. First is sort of like 'bank interest', with randomness. Suppose we invest 100 units of currency. Suppose each year there is a ...
124 views

Calculating the Risk Free Rate [closed]

I have an assignment and I have to calculate the risk-free rate with the following data: Stock A: E(R) = 10% ; Standard Deviation = 5%. Stock B: E(R) = 20% ; Standard Deviation = 10%. I also ...
461 views

Mark Joshi, The concepts and practice of mathematical finance chapter 6 exercise 6 [duplicate]

Suppose a stock allows a geometric Brownian motion in a Black-Scholes world. Develop an expression for the price of an option that pays $S^2 - K$ if $S^2 > K$ and zero otherwise. What PDE will this ...
235 views

Am I calculating my Kelly Criterion correctly?

I'm taking a look at my trading history over a particular time period and have 500 trades on with an win rate of 82%. My average win is $W$. My average loss is $L$. So am I correct in assuming the ...
708 views

Delta Hedging: Clarification example of the book “Hull, Options, Futures, and Other Derivatives” [closed]

By "Hull, Options, Futures, and Other Derivatives": Suppose that, in figure,the stock price is \$100 and the option price is \$10. Imagine an investor who has sold 20 call option ...
44 views

How to simulate the exponential law over an interval of the form [0,T]?

How do you simulate an exponential random variable over an interval $[0, T]$ with $T > 0$?
1k views

Is it possible to “steal” financial data on publicly traded companies off the internet? Legally, I mean, what is the truth about “data” as a property

What constitutes "stealing" when it comes to publicly posted financial data? I think there are three instances of this that we can individually vet: a.) you physically broke into a location or ...
105 views

Why is PCA/ML not used frequently in trading?

I'm curious why things like PCA/ML aren't use frequently in trading? Is there an underlying philosophy that prevent this? What I was thinking, was that if PCA worked for making money, then everyone ...
49 views

Process for mod of a variable that follows some Stochastic Process

Assuming a variable $v$ follows some Stochastic Process as below - $dv=\mu v dt + \sigma v dW_t, v \in \left( -\infty, \infty \right)$ I want to get the process of ...
82 views

Risk Neutral Pricing, a quick question [closed]

I am a newbie. The risk neutral pricing has the following formulation: $$P=\frac{\hat{E(d)}}{R}$$, But the discounted expected value has the formulation of: $$P=\frac{E(d)}{R}$$. The text book ...
100 views

Why do we make the Markov assumption on financial markets? [closed]

Why are Hidden Markov Models (HMM) a good fit to describe the behaviour of the prices of financial assets, when these models require that the underlying stochastic process satisfies the first-order ...
133 views

Hedging a stock with its index constituents?

Problem: select and weight 4 constituents of an index to hedge a particular stock I would appreciate any feedback on my approach, here is I would go about it: Create a new index of four ...
72 views

Stochastic Vol Mathematical derivation [closed]

I want to understand the mathematical steps done. Can someone please simplify the derivation of d(pi) from Pi? Thanks in advance.
253 views

Probability and statistics in Quantitative Finance

Certain types of traders attempt to repeatedly buy and sell the same asset for a profit over a short time period, such as high-frequency “market makers”. For example, if you can repeatedly sell a ...
81 views

Fourth moment of a itos integral

$I(t)=\int_0^t \sqrt sdW_s$ What is $E(I(t)^4)$
134 views

Separate market and limit orders from market depth/tick data

From the website https://www.algoseek.com/equities/, we can get a sample of the full depth market/tick data. From the paper https://arxiv.org/pdf/1710.03870.pdf page 8, I would like to extract the ...
192 views

Portfolio turnover [closed]

Really easy question, but I am having doubts. If you want annual turnover, and you have monthly weights, wouldn't you just do in excel: {=ABS(CurrentMonthsWeights-LastMonthsWeights)*12} for each ...
492 views

Lower bound for European put option prices — potential contradiction with BS

A classical no-arbitrage argument shows that for a European put with strike $K$ and time to maturity $T$, the price $p$ satisfies $$p \geq \max(0,Ke^{-rT} - S).$$ Is Black-Scholes in contradiction ...
342 views

302 views

Payoff of a butterfly c++

I would like to price options (call, put,, butterfly) with monte-carlo method, but actually I need the expression of the butterflay payoff; Could you ^please help me !
210 views

Building a personal computer for automated trading/analysis…what bottlenecks could I run into?

I've been trading forex and programming (I'm in college), but want to get into automated trading and analyzing data real-time to make decisions (and learning more about stats and math as a hobby). I ...
397 views

If I am very fast (less than 10 microseconds latency) what would be the first strategy to execute? [closed]

Let's assume I found the holy grail of low-latency trading (which I didn't). For educational purposes, what would be the first strategy I would direct my trading code?
1k views

Calculate the total returns from the total return index [closed]

I have the Total Return Index(RI) for several companies. I know that I can calculate the log retunrs with $ln(RI_t/RI_{t-1})$. Therefore my first guess would be to ...
50 views

In Short/Bull Put Spreads, why not sell a put at A and buy a put at B? [closed]

In Short Put Spreads, why buy an A put, and sell a B put? If $A < p < B$, you can be assigned to your B put, while your A put is worthless. Kevin Ott diagrams this below, but I added A, B. ...
69 views

Rolling Futures - VXX [closed]

I was reading this paper (https://www.cmegroup.com/education/files/deconstructing-futures-returns-the-role-of-roll-yield.pdf ) about futures rollover, and cannot figure out the meaning of the sentence ...
66 views

Options conversion/reversion arbitrage [closed]

I'm trading bitcoin option and i'm trying to find arbitrage opportunity with a synthetic short/long and a long/short future position. The options are europeans style and settled in BTC. The contracts ...
63 views

How is market depth data useful

I was wondering how market depth data is useful if the orders which change the price would not be available . If we consider the orders which change the price , these are the orders where the bid on ...
How can I convert the following process to a standard Brownian Motion? $$\mathrm{d}r_t=(a-br_t)\mathrm{d}t+\sigma\sqrt{r_t}\mathrm{d}W_t$$