0
votes
1answer
49 views

GARCH Model Constant in Regression

When regressing a variable on a constant of 1, the coefficient of this constant is the mean. However, when I specified that the residuals follow a GARCH(1,1) model, the coefficient of the constant ...
3
votes
2answers
74 views

How can I calculate the fair value of an ETF using the current price of each of its holdings?

Say, for example, I'm looking at the Vanguard Information Technology ETF (VGT) If I have the current market price for each of its holdings, and related information ...
2
votes
2answers
92 views

Option pricing, origin of formula $\Pi( t,X)= E^{\mathbb{Q}}\left[e^{-\int_{t}^{T}r_s\,ds} X| \mathcal{F}_t\right]$

Imagine a model with stock prices and dividends of these stocks, as well as a market bond with associated short rate process. It is known that this model is arbitrage-free if there exists an ...
2
votes
2answers
97 views

Trading with Inflation, Unemployment, Trade Deficit Information

I am trying to create a model for inflation for trading purposes. In his book The Market: Practice and Policy S. Nickell presents a model that relates unemployment, inflation and trade deficit. His ...
-1
votes
0answers
30 views

What is the value of the hedge under risk neutral measure?

Given: $$S_1(0) - S_2(0) = K $$ $$ V(T) = S_1(T) - S_2(T) $$ Let $D(T)$ be the discount process. $$ V(t) = K/D(t) $$ Show that the value of hedge is $$K/D(t)$$ I am looking for suggestions as to ...
1
vote
0answers
54 views

Backtesting Long/Short Market Neutral Z-Score Strategy with Custom Factors and Custom Stock Universe

So I've managed to backtest simple strategies, like MA, RSI and some fundamental ones (P/E ratios etc) but Im stuck at my last strategy. Here is some information: Tools: Excel and Python (also a ...
1
vote
0answers
19 views

Should the number of Markowitz Optimization steps be counted as backtest trials?

I'm backtesting a strategy that involves monthly investments in a few stocks out of a given set, that is, each month some of the stocks are shortlisted from an index and a long position is taken in ...
1
vote
1answer
59 views

construct volatility smile based on historic observations

So I calculated historic volatility/skewness/kurtosis for a commodity. I now would like to construct a volatility smile that reflects this historically realized distribution. I tried using some ...
2
votes
1answer
32 views

Extended Areas on Stochastic Volatility Modelling

I'm interested in the areas surrounding Stochastic Volatility Modelling. I've read up on the main models that are prominent in the literature (Hull White, Heston, SABR) but I was wondering what the ...
1
vote
1answer
66 views

pricing the discount zero-coupon bond under a jump-diffusion model

I am going to get the price of a zero coupon bond in a jump-diffusion model. The dynamic of interest rate as follow $$dr_t=\kappa(\theta-r_t)dt+\sigma\sqrt{r_t}\,dW_t+d\left(\sum\limits_{i=1}^{N_t}\,...
1
vote
1answer
33 views

Find the parameter $d$ of the Affine Option Pricing Model in Duffie, Pan and Singleton (2000)

According to Duffie, Pan and Singleton (2000) for any real number $y$ and any $a$ and $b \in \mathbb{R}^n$, the price of a security that pays $\exp(aX_t)$ at time $T$ in the event that $bX_t \leq y$ ...
1
vote
1answer
31 views

Pricing Barrier Options with Rebates

How are rebates factored into the Black-Scholes analytical solutions to pricing barrier options? In Hull's book, he does not have rebates factored into the formulas. Can someone point me to a paper ...
1
vote
2answers
50 views

Very Simple Log Return Correlated Stock simulation

Suppose we have 3 stocks which follow GBM. We are given the distribution of the daily log returns which is multivariate normal. Suppose I want to sample the stock price tomorrow ($\Delta t = 1$ day). ...
1
vote
0answers
33 views

Model Free VIX Calculation in Python

I have previously seen this implementation and had meant to replicate it, but can't find it any longer. Does anyone know of a python implementation of the CBOE Volatility Index? Yes, the white paper ...
1
vote
1answer
33 views

Trader Workstation on Ubuntu cannot be connected to via the API

I am using ibPy to connect to TWS on a fairly fresh ubuntu machine. I have been successful in logging into the paper trading account and submitting buy and sell orders programatically via the ibPy ...
2
votes
0answers
40 views

How to understand quadratic finance or practice of Value-at -Risk(VaR)

We define the following notions for a jointly normally distributed random vector $P=(P_1,...,P_n)$ with f the density function. $$\mu=\int_{-\infty}^{\infty}(x_i-\mu_i)f_i(x_i)dx_i$$ $$\sigma^2_{ij}=...
3
votes
0answers
47 views

How to calculate this swap rate

What is the 2x5 swap rate? here 2x5 swap rate refers to the 3-year swap, 2 years forward.
5
votes
2answers
54 views

Price and constant hedging portfolio for straddle: $X=|S(T)-K|$

wondering if somebody could check my answer for a homework question! Given a straddle, characterized by its pay-off at maturity $X=|S(T)-K|$, I am asked to find the price of the (simple) claim at any ...
1
vote
2answers
91 views

Black-Scholes PDE & Terminal Condition

Just a quick question I was hoping someone could shed light on. So far I am familiar with the Black-Scholes PDE with the terminal condition at time $T$ been $V(t=T,S)=(S-K)^+$. I also understand ...
3
votes
0answers
61 views

Trading signal strength: [-1 to 1] or [predicted return]?

In the context of a backtesting engine, is it better to have strategy generate trade signals in the range from -1 to 1 or as exact predicted returns (e.g. -12% or 26%). The difference lies in how to ...
1
vote
0answers
30 views

Could someone please share the Matlab code for the stochastic volatility jump diffusion option pricing model? (Bates model) [closed]

I have not been able to write a Matlab code for the Bates model without errors. Could someone share theirs please?
3
votes
0answers
60 views

what is the minimum capital necessary for quantitative/automated/algorithm trading? [closed]

I mean from my home for myself I have a degree in statistics so I know time series, predictions, R ... I would like to design statistical model for trading with R I don't ask for trading strategies, ...
1
vote
0answers
43 views

Transition Between Volatility Regimes

Emanuel Derman wrote a great paper in 1999 about volatility regimes and the adjustments the market makes during these periods (sticky strike, sticky implied tree, sticky delta, etc). Has any ...
4
votes
2answers
130 views

Is it possible that under Black-Scholes: $\ln S_{T} \sim N \left ( \ln S_t - \frac{1}{2}\sigma^2(T-t), \sigma^2(T-t) \right )$

I have a slide on which there is written that under Black-Scholes model: $$\ln S_{T} \sim N \left ( \ln S_t - \frac{1}{2}\sigma^2(T-t), \sigma^2(T-t) \right )$$ Now, here there is a good explanation ...
1
vote
1answer
28 views

Two fund separation when there's a risky asset?

I am currently reading a book which begins its portfolio theory section with the case with $n$ risky assets where it proves that 2-fund separation applies (any minimum variance portfolio is a linear ...
3
votes
2answers
48 views

What's the explanation for the formula for the volatility of a stock / volatility of the continuously compounded return of a stock?

I am self-studying for an actuarial exam, Models for Financial Economics. It's stated as a given in my manual that $\sigma$ is the volatility of the stock, $\sqrt{\text{Var}(\ln(S_t/S_0))}$ and that ...
1
vote
0answers
22 views

Architecture and Infrastructure for Robo-Advisor [closed]

Does anybody have any knowledge of Architecture and/or Infrastructure needed for building your own Robo Advisor. I am looking for directions to get in-depth knowledge for building your own Robo ...
1
vote
0answers
46 views

Number of mortgages in a MBS

Is it possible to know the typical number of mortgages that can be packaged into a MBS product, e.g. a pass-through MBS, or an agency backed TBA. I think the minimum size is \$1-million but if a ...
1
vote
0answers
45 views

How can we observe volatility smile from the market. Drawbacks of Heston Stochastic Volatility Model

Here are two questions related to implied volatilities. a) The set up here is for an European option. We can get its implied volatility smile from calibration, the question is why could we also ...
3
votes
2answers
66 views

Questions on arbitrage

I have the following questions about arbitrage that I am unsure of. Will an inverse term structure rate imply arbitrage possibilities? Will negative zero coupon rates imply arbitrage possibilities? ...
1
vote
1answer
65 views

Cox-Ingersoll-Ross

I am looking at a displaced CIR model and try to calibrate it to market data. I think my results looks reasonable but would like to sense-check with other studies. Does anyone know what "reasonable" ...
1
vote
0answers
34 views

A question on option pricing [closed]

Calculate the value of 9-month American call option to buy 1 million units of a foreign currency using a three-step binomial tree. The current exchange rate is 0.79 and the strike price is 0.80 (both ...
2
votes
2answers
83 views

From discrete time series models to continuous

Is it possible to convert an SARIMA model to a continuous model? If so, what is the methodology to do that?
1
vote
1answer
45 views

Difference between Deterministic Volatility Function approach and Ad Hoc Black Scholes?

I am thoroughly confused after reading Dumas, Fleming & Whaley (1998) "Implied Volatility Functions: Empirical Tests". Both the Ad Hoc BS Model and the Deterministic Volatility Function ...
1
vote
0answers
27 views

Replicating portfolio: initial portfolio?

I have a bit of trouble understanding how to determine the replicating portfolio of a call using just a stock and the riskfree asset. I have times $t = 0,1,2$, and at time $2$, we have $3$ payoffs ($...
0
votes
2answers
38 views

Valuation growth rate for perpetuity

What would be reasonable rates of return for the computation of perpetuity in firm valuation? I tend to google FMI's expected World GDP growth rate, but I can't always find results. Would someone ...
4
votes
1answer
84 views

What if: Negative interest on an overdrawn bank account?

Theoretical question: Consider if a bank account had a -12% yearly interest rate, and an account was currently overdrawn to a balance of -$100. What would the bank do to the -$100 balance after one ...
2
votes
0answers
13 views

US Rule versus Actuarial Method for calculating interest

I'm trying to understand the difference between the actuarial method and the U.S. Rule for calculating interest. I think the difference is that the actuarial rule adds unpaid interest to the principal ...
1
vote
2answers
40 views

cumulative return calculation, disagreement

A friend of mine and myself are having an argument on how to correctly determine cumulative return. The dataset has monthly return data and we are trying to determine the 6-month cumulative return. ...
2
votes
0answers
61 views

Risk neutral probability and forecasting

When our goal is pricing of derivative products we, due to no arbitrage conditions, have to use the risk neutral probability. In other side if we have risk management purpose we have to use the “...
1
vote
1answer
54 views

Why does the correlation between r and V in Longstaff and Schwartz 1992 model is positive?

I am reading the Longstaff and Schwartz's 1992 and 1993. From $r = \alpha x + \beta y$ and $V = \alpha^2 x + \beta^2 y$. It was mentioned in the paper that the $r$ is positive correlated with $V$. ...
4
votes
2answers
130 views

Are two stochastic processes independent if the Wiener processes inside are uncorrelated

Assume there are two stochastic processes: $dx_t = \alpha_1(x_t,t)dt + \beta_1(x_t,t)dW^1_t$ and $dy_t = \alpha_2(y_t,t)dt + \beta_2(y_t,t)dW^2_t$. Does $dW^1_t\times{dW^2_t} = 0$ imply that $\...
2
votes
1answer
34 views

Help understanding factor modeling, solving for residuals

I am trying to understand and implement a factor model, and I think I might be having some issues. I am trying to solve for the residuals in the equation: $$ R_{i} = \sum_{A=1}^{K}\beta_{iA} f_{A} + ...
0
votes
1answer
71 views

What models / methods are used in practice in derivative pricing?

I wrote my bachelor thesis about European Option Pricing under Stochastic Volatility and Jump Diffusion and am now near the end of my MSc in Quant Finance. As i want to write a "potential job"-...
1
vote
0answers
22 views

How to calculate monthly Return from a Momentum Strategy with overlapping Holdingperiods?

I replicate a Momentum Strategy from Rey and Schmid (2007) "Feasible momentum strategies" based on the idea from Jegadeesh and Titman (1993). I only buy the single stock with the highest past return ...
0
votes
2answers
42 views

How to setup a back test step by step?

I would like to setup a back test for Indian equities, Kindly help out with step by step procedure, No need to go into details, outlining of procedure are enough in bullet point, I will research ...
6
votes
2answers
62 views

SABR Model Closed Form Solution

I've been researching the SABR model and one of the main benefits it seems is that you can obtain a closed for solution of the implied BS volatility in certain cases. In all the papers I've read, I ...
1
vote
2answers
56 views

Put Volatility Smiles and Implied Volatility

I have been observing the option chains of put options with differing maturities. I have noticed that those puts with a close expiry date have the steepest volatility smiles. Can someone please ...
0
votes
1answer
55 views

Delta Hedge, does large stock move produce a loss?

I dont understand how MM protect themselves from large moves in underlying while being delta hedged. Example: MM sels 1 ATM put and sells 100stock (delta = 1) as a hedge. Now what will happen if next ...
3
votes
1answer
54 views

Realized Vol for 15 min interval using second Data

I would like to calculate realized volatility for a 15 min period. Most of the literature I looked up shows how to construct daily realized volatility using intraday data. These literatures does use ...

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