All Questions

2
votes
3answers
633 views

What mathematical theory is required for high frequency trading?

I am an applied math postdoc and I have been presented with the option of leaving academia to work in high frequency trading. I wanted to get a feel for the field and the theory underlying it so I ...
0
votes
0answers
4 views

How frequently is local volatility calibrated to implied vol surface, in practice?

This has two related questions - How frequently do equity derivative traders re-mark the implied volatility surface - (i) once a day (e.g. at start of trading day, or end-of-day), or (ii) ...
0
votes
0answers
6 views

How to add annualized quarterly returns?

I have four quarterly returns that have all been annualized. How do I calculate the annualized return for the year from these values? Or do I need to back into them to get the holding period returns
1
vote
1answer
21 views

American Put Option Pricing

I am trying to solve a question of American Put Option pricing as below. Build a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with:...
-4
votes
0answers
18 views

Pseudo-math in famous quant finance book. How do I interpret this?

I am reading Jim Gatheral's The Volatility Surface, and am astounded at some of the math. It's not even math, it's pseudo-math. Please provide an explanation to the following mumbo-jumbo. On page 27,...
3
votes
1answer
71 views

What is the easiest way to learn Option pricing with PDE?

I was reading about Ito's formula and Girsanov theorem, but I am still struggling to grasp how in reality these are combined to compute the price of an option. What are the main source to understand ...
1
vote
0answers
13 views

How would one go about pricing a FX future?

What model/equations would I require to calculate the price for a foreign exchange future? This is in an attempt to mitigate foreign exchange risk. Also, how could one measure a business's exposure to ...
1
vote
1answer
61 views

Understanding the ZABR model (an extension of SABR)

http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf In this acticle the SABR model is first presented in another form ( see equation 7 in the article ) and then extended to the so called ZABR ...
0
votes
0answers
18 views

high quality daily data [duplicate]

I am analysing some trading strategies, so lots of high quality data is needed. I have been using yahoo finance which provides a lot of high quality daily data on stocks and indices. Currently I am ...
2
votes
2answers
232 views

What are some examples of non-solvable SDE where Monte Carlo discretization is necessary

Reading Glasserman - "Monte Carlo Methods in Finance" it says in the introduction to Chapter 6 - Discretization Methods, that moste models arising in derivatives pricing can be simulated only ...
1
vote
0answers
18 views

Hull White Equation Derivation

Hello I need your help. I found the formula for deriving $A(t,T)$ and $B(t,T)$ in Hull White paper is like this $BB_{tT} - B_{t}B_{T} - B_{T} = 0$ and $ABA_{tT} - BA_{t}A_{T} - AA_{t}B_{T} + \frac{1}...
-3
votes
0answers
42 views

What does this formula in Jim Gatheral's book mean?

From Jim Gatheral's "The Volatility Surface", on page 11 he introduces a formula (formula (1.7) at the bottom). Is he talking about the "future value of the option"? I do not understand the "future ...
8
votes
1answer
232 views

Heston model reparametrisation

It is well-known that calibrating Heston to the vanilla market is not as easy as it seems: some parameters are "interdependent" and the objective function exhibit plateaus in the parameter space (at ...
2
votes
0answers
15 views

Proof standard Brownian Motion under change of measure

Let's split the usual time horizon $[0,T]$ like $0=T_{0}<T_{1}<\dots<T_{n}=T$ and consider the bond price $P(t,T_{i})$ for $i=1,...,n$. We assume $$\frac{dP(t,T_{i})}{P(t,_{i})}=r_{t}dt+\xi_{...
0
votes
1answer
16 views

BHAR Event Study - Index

I want to perform a BHAR event study. For that, I subtract the compounded returns of a benchmark portfolio from the respective stock. Is my assumption right, that I can simply take any underlying ...
0
votes
1answer
23 views

Getting sets of random correlated variables

For the training of a machine learning model I need to add additional features (macro variables), and these features are correlated. I need to run the model N times adding these features with random ...
3
votes
0answers
27 views

Annualization of higher order Co-moments

I'm developing a dynamic portfolio optimization procedure based on the implementation of the Modified sharpe ratio. The mentioned ratio depends, among other factors, on the skewness and kurtosis of ...
0
votes
0answers
29 views

Realized volatility transformation [on hold]

After calculating the realized volatility as $log\Big(\sqrt{\sigma_R^2}\Big)$ and forecasting some datas as $log\Big(\sqrt{\sigma_R^2}\Big)$, how can we get back to the $\sqrt{\sigma_R^2}$ ? it's ...
0
votes
0answers
19 views

Zero rate computation in Quantlib

I am trying following code, zerorates which is received is different than I expect. Can someone suggest where am I going wrong? ...
0
votes
0answers
23 views

Going from normal to Log-normal implied volatility

Let's denote the Implied normal volatility (Bachelier) as $\bar{v}$, and the implied log-normal (Black Scholes) as $v$. When everything else is known (spot, strike, maturity, rates etc) how can you ...
1
vote
1answer
47 views

Why do Factor Models set up their factors differently from regression?

While this may be awkwardly-titled, I hope that my question becomes clearer upon reading. So this is what I gather about Factor Models: they are statistical models set up to explain the returns, ${...
2
votes
1answer
50 views

what are the underlying transactions for SOFR?

Recently I am reading about SOFR (Secured Overnight Financing Rate), which is projected to replace LIBOR to be the reference for risk-free rate in the market. But I still don't understand or imagine ...
8
votes
1answer
498 views

Transforming 3M volatilities into 6M volatilities in EUR forecast curves

I have implemented a stripping algorithm to extract forward volatilities from cap/floor flat volatilities for different currencies. I am however struggling a bit when implementing a method to convert ...
2
votes
2answers
37 views

How to calculate necessary gain to compensate a loss in a financial transaction?

(Feel free to suggest the correct Stackexchange community - or otherwise - if this is not the correct one) When trading financial markets, a gain of x%, won't ...
3
votes
2answers
3k views

Pricing a fixed rate bond in Quantlib Python

I'm trying to implement a pricing model for fixed rate bonds with the code below. ...
1
vote
1answer
39 views

Why is the volatility of an Ito process not the square root of its variance?

The volatility $\sigma$ of an Ito process $dS_t = r S_t dt + \sigma S_t dW_t$ is not the square root of its variance. But you often hear that "volatility = standard deviation". What's going on here?...
1
vote
1answer
29 views

Why the variance of a process is $\left( \frac{dS_T^2}{dt}\right)^2$?

Consider an Ito process $dS_t = f(t,S_t) dt + g(t,S_t)dW_t $ What is the reason that we can compute the variance as: $\sqrt{VaR(S_t)} = \frac{(dS_t)^2}{dt}$
1
vote
1answer
37 views

Rationale for likelihood function parameter choice in Black-Litterman model?

So we are interested in a PDF for equilibrium returns given the views. Why do we choose our view means as the mean parameter and observed market covariance as the covariance parameter? Seems a bit ...
1
vote
1answer
75 views

Are questions in Joshi's book really asked at Quant interviews?

I am reading some questions in Joshi's book on Quant Job Interview Questions, and am perplexed at some of the questions in the book. Some of them are extremely easy (like, "explain the Black Scholes ...
1
vote
0answers
14 views

How is hypothesis testing work in population sampiling?

I am learning the basics of quant trading from quantconnect's tutorial Confidence Interval and Hypothesis Testing. I understood the first part of the article but I dont understand "Hypothesis Testing"...
1
vote
1answer
162 views

A volatility model developed by JP Morgan

I am quite confused with this predicting volatility equation: σ2t = βσ2t-1 + (1-β)ε2t Here is a section from Capital Market Expectations: CFA Level 3 Volume 3 Curriculum (page 27) https://ibb.co/...
3
votes
1answer
59 views

Estimating a Yield Curve in a country without Bond Stripping

I am currently working under estimating a Yield Curve. From my understanding common procedures to construct a yield Curve like Nelson Siegel have the input of a series of different zero rates and ...
3
votes
1answer
182 views

Mixing Black Scholes with SABR

I am new to the whole concept of stochastic volatility so I am experimenting with option pricing. I think the concept is really difficult to understand / grasp. I was wondering if the following ...
7
votes
3answers
2k views

Forward implied volatility

Can one price accurately by only using vanilla options a derivative that is exposed/sensitive mainly to the forward volatility ? If it is impossible, why do we hear sometimes "being long a long ...
3
votes
1answer
35 views

How to prove martingality of forward rate under T-forward measure

Let $P(t,T)=\mathbb{E}_{Q_{R}}[e^{\int^{T}_{t}r(u)du}|\mathcal{F}_{t}]$ be the price of a 1-euro zero-coupon bond with maturity $T$ and $r(u)$ the interest rate process. Consider the the forward rate $...
95
votes
17answers
17k views

Video lectures and presentations on quantitative finance

What are your favourite video lectures, presentations and talks available online? A few rules: Must be related to quantitative finance. No Economics 101 courses, please. Try to avoid DIY lectures ...
1
vote
0answers
15 views

Does EFP (Exchange Futures for Physical) Involves Cash Exchange?

I am new to the concept of Exchange Futures for Physical (EFP). According to some sources (link), An Exchange for Physical (EFP) is a transaction involving the simultaneous exchange between two ...
3
votes
1answer
53 views

How to comprehend this notation?

I learned mathematical finance from Bjork's Arbitrage Theory in Continous Time, and never once did I encounter the "quadratic variation"-thingy with the angle brackets. So now that I am reading ...
1
vote
1answer
22 views

Is the undiscounted value process of a Euro call option under Bachelier model a Martingale?

Assume that $c_t$ is the UNDISCOUNTED price process for a European call option in Bachelier model. In Bachelier model call option pricing formula the formulas is discussed. The undiscounted value ...
2
votes
3answers
4k views

Why is the value of debt modeled as a short put option in Merton's model?

Can someone give me an intuitive understanding of why the Merton model models the value of the debt from the lender's point of view as a short put with a risk free bond? I'm not well versed in this ...
1
vote
0answers
33 views

transactions costs and leland modified volatility

When there are transactions costs, we are in a situation of incomplete market. What does the modified volatility of Leland (Option Pricing and Replication with Transactions Costs, 1985) bring us? can ...
1
vote
0answers
29 views

Fixed Income Portfolio Optimization

I'm trying to solve for a maximum sharpe ratio portfolio in the fixed income space. To do so, i use CVXPY in python. I use this Paper as reference. This is my "setup": ...
1
vote
1answer
84 views

Calculation of Combined IRR

How to calculate combined IRR for two different cost of funds? The emi (Equated Monthly Installment) amount, whether it is calculated separately or based on the combined IRR should be same. I tried ...
1
vote
2answers
177 views

Understanding Forex Positions

I am new to forex trading and using an Oanda free practice account to play with it. However, I'm not understanding a few things. When I buy or sell a currency pair, am I buying/selling a currency or ...
2
votes
0answers
23 views

Mean directional accuracy and zero

I'm trying to use mean directional accuracy to evaluate my directional predictions in back-test, but it can't deal with realised directions which are 0, due to the comparison of the signs of ...
1
vote
0answers
20 views

Calculating management fees paid during the last 12 months

I'm looking for a way to calculate the total management fees paid by a customer during the last 12-months. I'm taking the following assumptions: The total accumulation as of today is A The monthly ...
1
vote
2answers
82 views

Where can I get the actual info about how many stocks are there in markets all over the world?

I need to test an algorithm for large-scale data in stocks market. I wanna know how many stocks are there all over the world and the data source.
2
votes
0answers
17 views

Units of measurement for Minimum Variance Hedge Ratio

The minimum variance hedge ratio is given by $h=p*\frac{\sigma_S}{\sigma_F}$. I was wondering if you wanted to calculate the S.D yourself and the spot prices were in Dollars per barrel while futures ...
6
votes
1answer
9k views

What is the equation for Garman-Klass volatility?

I want to calculate realized/historical volatility for the underlying products of various options using the Garman-Klass estimator, but I can't see to find an equation, although I know it involves ...
1
vote
0answers
42 views

Newbie question on Net Present Value with Constant Growth

Newbie here, trying wrap my head around on why this doesn't add up: Calculating the discounted cash flow of a perpetuity paying $1000 per year, 15% discount rate and 5% growth. If I calculate from ...

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