2
votes
1answer
75 views

Solving a backwards heat equation using stochastic calculus

Given the PDE $$\frac{\partial F}{\partial t} + \frac{1}{2}\sigma^2 \frac{\partial^2 F}{\partial x^2} = 0$$ with condition $F(T,x) = x^2$, one can use the Feynman-Kac formula to arrive at $$F(t,x) =...
0
votes
2answers
53 views

Black Scholes Implied Volatility -> Put call parity

The theory says that the put and call with the same maturity and strike have the same volatility. I have been resolving the Black Scholes equation after IV using equity and fx market data and I can ...
1
vote
1answer
131 views

how to do interpolation in the term structure of volatility surface?

everyone~ I am a newbee in the quantitative finance and I meet a problem in working out an equity option volatility surface. We use the reasonable market data to derive the implied volatility, then ...
1
vote
1answer
38 views

how to choose a price adjustment, a roll date and a data center for my trading strategy?

I have many doubts about Which roll date and price adjustment should I use. I need to backtest like 50 diferents futures. 6 index(mini sp500, Nikkei 225…), 10 Agriculture (soybean, Oat, Corn….),3 ...
0
votes
0answers
27 views

CIR model, realistic parameters and usage

I'm currently working on SDE's, in particular with mean-reversion processes like CIR and Vasicek. The definition of the CIR model is \begin{equation} dX_t = \kappa(\theta-X_t)dt + \sigma \sqrt{X_t}...
0
votes
0answers
27 views

Download DGS3MO from FRED with getSymbols - error

I follow the course "Mathematical topics in finance" from MIT courseware. I opened R and rendered Dr. Kempthorne's Case Study 3: Time Series from September 30, 2013 I am able to render the code and ...
2
votes
1answer
101 views

Implied Volatility in Heston Model

recently I started reading the interesting book about option pricing in the stochastic volatility world from Lewis. He gives very interesting and detailed insights about this topic in general. However ...
-2
votes
1answer
78 views

Why do banks offer options? [closed]

I have only taken one introduction class in finance. However we came along opinions, their pricing, etc. We only contemplated being the buyer of a option. If everything works for you apparently you ...
1
vote
0answers
86 views

Interview questions pictures [closed]

I got this questions which is quite interesting, I am in a museum, there are 100 rooms (numbered from 1 to 100) in this museum and each room has a picture in it. I go visit each room in the ...
2
votes
3answers
85 views

residual correlation remains after seasonal lag added

I'm attempting to model operating margins and a time plot indicated that the series may follow an autoregressive process. I initially fitted data to an AR(1) model and it appeared that residual ...
0
votes
1answer
77 views

State Variables in a Bellman Equation

Can anyone explain to me exactly what a state variable is in a Bellman equation?? $$ V(x,y)=max\space u(c)+\beta V(x',y')$$ In some models with capital savings it's the capital $k_t$ you walk into ...
2
votes
0answers
34 views

European call option delta and maximum principle

From comments, the maximum principle for parabolic PDE can be used to show that the European call option delta cannot be greater than 1. I am looking forward to such derivations.
3
votes
1answer
94 views

How do one solve $ \int_t^T \exp[\int_0^u-( r-\delta_s)ds] dW_u $? Double integral with general deterministic function $\delta(t)$

How do one solve $ \int_t^T \exp[\int_0^u-\left( r-\delta_s\right)ds] dW_u $ ? $\delta(t)$ is a general deterministic function. $r$ is constant.
2
votes
2answers
129 views

$E[F_T] = F_0 \ \rightarrow \ \text{or} \ \leftarrow \ p = \frac{1-d}{u-d}$?

From Ch 12 in Hull's OFOD, we compute the risk-neutral probabilities for a futures contract: Later in Ch 17, futures options are valued, and we have the same result: In relation to ...
3
votes
2answers
249 views

Pricing when arbitrage is possible through Negative Probabilities or something else

Assume that we have a general one-period market model consisting of d+1 assets and N states. Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option, with ...
1
vote
0answers
40 views

Is the European call option delta an increasing function of the spot?

In the Black-Scholes' setting, the delta hedge ratio of a European call option is given by $N(d_1)$, which is an increasing function of the underlying equity spot $S_0$. Does this property hold ...
0
votes
0answers
14 views

Magnitude of Predictors on Logistic Regression

We are using logistic regression for calculating delinquency. We know what the major predictors are, but we don't know how to quantify the impact of each of the major predictors. We know how to rank ...
1
vote
1answer
40 views

Pricing of American Deriviatives

Reading the book by Andrea Pascucci "PDE and Martingale Method in Option Pricing" I am struggling with a very simple issue. Suppose we want to find the price of an American derivative $X$ in an ...
0
votes
2answers
85 views

Using Forward or Spot rates for NPV?

I have to calculate the NPV for Capital Budgeting in a project with annual cash flows discounted by a risk - free interest rates 1.Instead of using a constant interest rate, should it better to use ...
2
votes
0answers
30 views

How does the diameter of the spatial grid affects the solution of a Crank Nicholson algorithm?

this is my first question so I hope I express myself clearly. I'm trying to implement an Implicit and a Crank Nicolson algorithm for the generic PDE $\partial_\tau u(\tau,x)+a \partial_x^2 u(\tau,x) +...
0
votes
0answers
34 views

Inverse Laplace transform

I'm trying to compute the inverse Laplace transform of the function gam below ...
1
vote
1answer
47 views

Bid/ask and volumes from ITCH feed, what is the most efficient way to do this?

I am very green when it comes to programming. I am doing a market microstructure study where I need to investigate how certain stock characteristics affect their liquidity. I have Nasdaq OMX ITCH Feed ...
1
vote
1answer
126 views

Historical book value data for S&P 500

In Graham's Intelligent Investor, he calculates a metric Earning/book value. I would like to calculate the same ratio in modern times (1960-2015) but am having trouble finding this data. I have found ...
0
votes
2answers
59 views

Yield curve interpolation at (very) short horizons

I'm struggling to find much information about yield curve interpolation for sub-yearly horizons. Say, one-two months. It seems to be the area where the curvature is usually nontrivial, while after ...
1
vote
0answers
74 views

Portfolio Optimization with equal weight for assets selected

I have a data frame of bets, with 1 being a win and 0 being a loss. These bets are correlated so I cannot just pick the highest winning percentage. Goal is to get 2 optimizations, 1 for max sharpe ...
0
votes
0answers
37 views

Solving inequality constraint

I am trying to solve the following inequality constraint: Given time-series data for N stocks, I am trying to construct a portfolio weight vector to minimize the variance of the returns. the ...
0
votes
0answers
47 views

Probability of reversion for cointegrated variables

I ran a Johansen test to figure out the cointegrating relationship between two variables $x$ and $y$, forming the equation $z=ax+by$ using the eigenvectors. The values are computed using from time ...
0
votes
1answer
34 views

Calculating Volatility Parameter using Closing Prices [closed]

Say you have 3 closing prices... 101 100 102 How would one calculate the standard volatility parameter using these values? I am quite confused, it seems simple enough though.
0
votes
1answer
45 views

Motivation: Stochastic Interest rate model

what is a reason that someone might be interested in a stochastic-interest model such as the Chen model? Also can you provide me with a link to an easy to read motivational paper/part of a paper on ...
2
votes
1answer
108 views

Risk Manager must-know list

What are the products, concepts, and models a risk manager must know? I'm not looking for an exhaustive list, but rather a general list as the one in Paul & Dominic's Guide To Quant Careers: ...
3
votes
4answers
219 views

Calculate theoretical forward price of a stock

The current price of a stock is USD400 per share and it pays no dividends. Assuming a constant interest rate of 8% compounded quarterly, what is the stock's theoretical forward price for delivery in 9 ...
1
vote
1answer
56 views

How to change to risk neutral measure in a mean reversion process?

For example, in the Ornstein-Uhlenbeck process do I just replace the drift term with the risk free rate, like in the GBM case?
1
vote
2answers
106 views

Stochastic process theory question

*S follows a process $dS= mSdt + oSdz$ where m and o are constant. What is the probability followed by $ Y=(Se)^{(r-t)} $. If S follows a process $ dS= k (b-S) dt + oSdz $ where k, b, o are ...
2
votes
2answers
207 views

Forecast of volatility

What are the well known methods for forecasting (daily - weekly - monthly) volatility of a stock price? How about a bond price? Let's say I have in my disposition the price time series at a very high ...
1
vote
1answer
156 views

Delta Hedging for 2 Factor Models

If the value of an option at Maturity is what is the off-setting position you take for X and Y, if you are i)Long Call of the option ii)Short Call of the option iii)Long Put of the option iv)Short ...
0
votes
0answers
19 views

How Current are Google Finance & YQL Sock Information

When viewing a specific stocks information on Google Finance and Yahoo Finance- how old/current is the stock information (Price, offer, bid, etc)? I've heard some providers offer information that is ...
0
votes
1answer
47 views

Why is the forward rate used for the underlying in Black's model?

Why is the forward rate suitable for being used as the underlying in Black's model? Thanks
2
votes
2answers
86 views

$ \mathop{\mathbb{E^{}}}\left\lbrace 1_{S_T > K} \; S_T \right\rbrace $ ? Exp. of an indicator funct and a diffusion with non-proportional vol

How to compute $ \mathop{\mathbb{E^{}}}\left\lbrace 1_{S_T > K} \; S_T \right\rbrace $ ? where $ dS_t = S_t r dt + \sigma dW_t $ and $ 1_{S_T > K} $ is the indicator function being one when ...
2
votes
1answer
72 views

Estimating Carma(2,1) parameters (using yuima package)

I am very new to R, and particularly to the yuima package, so I was hoping someone would be able to help me. I have some data (daily prices) that I wish to fit to ...
0
votes
0answers
19 views

Question in the proof of “Optimization of conditional value-at-risk”

I'm reading the paper "Optimization of conditional value-at-risk" by Rockafellar and Uryasev. The state two theorems within the paper which are proven in the appendix. Let me introduce some notation ...
1
vote
1answer
39 views

Optimal Financing Mix: Cost of Capital Approach

According to Cost of Capital approach to optimal financing mix we can calculate Cost-of-Capital-minimizing $\frac{D}{E}$ ratio as follows: $\frac{D}{E}_{opt} = argmin_{\frac{D}{E}}WACC$, where $...
0
votes
0answers
25 views

Effect on variance of change of measure

My current understanding: (a) changing the probability measure of a diffusion process does not change the variance. (b) for a general stochastic process the variance may change. Please confirm whether ...
0
votes
0answers
36 views

BLS v2 API took 20+ minutes to publish data where is immediate data available?

First, I should state that I built a Java program that uses HTTP Components to keep in sync with server time for my broker. Once 7:29:59 comes around the program ...
4
votes
2answers
625 views

How many monte carlo runs do I need for pricing a Call?

I have to price several calls using Monte Carlo. Obviously, there is a huge tradeoff between the number of runs and the fair price of the call option. I know I can check how the approximation changes ...
2
votes
1answer
79 views

Brownian motion. Solve stoc. integral by using Ito's lemma

I want to show that following statement is true by using Ito's lemma to solve stochastic integrals: I define the functions in Ito's model: a()=0, b()= (2wt-2)^2. f(t)=Integrate[(2wt-2)^2] Then df=(b^...
6
votes
2answers
130 views

Realized variance in SVJJ (Heston with jumps) model

I am working with the stochastic volatility model with jumps in both the price and volatility dynamics, ie. the risk neutral dynamics are of the form: $\mathrm{d}V_t = \kappa(\theta - V_t)\mathrm{d}t ...
0
votes
0answers
30 views

Measuring strength of correlation for bivariate time series

In case of a bi-variate time series with both I(0) how do I measure the strength of co-relation. I am looking for measure similar to R-squared but ideal measure may not be one of the variants of r-...
2
votes
0answers
48 views

When to use SV or a GARCH model

So i have been searching for this answer for a question if there is a rule or something that would say when to use GARCH type model or use an stochastic volatility model to predict the volatility of ...
0
votes
0answers
63 views

How to use genetic algorithms to optimize moving averages

I'm working on a school project that attempts to optimize moving averages using genetic algorithms. From what I understand about moving averages, it is an average over a certain length of time. To ...
0
votes
1answer
55 views

Factor model to Portfolio optimization

By using the Fama and MacBeth methodology, I have identified the significant factors that explain the returns of my stocks. Now, I want to build a portfolio and backtest it. For that, I am trying ...

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