5
votes
4answers
199 views

Why is $C(t,S_t)/B_t$ a martingale?

In the derivation of the Black-Scholes formula given by Joshi (extract below), he says $C(t,S_t)/B_t$ is a martingale. Why? I understand this can be deduced from the Black-Scholes PDE since the drift ...
1
vote
0answers
29 views

Issue with Naive Bootstrapping (US Government Bonds)

I am using the formula here to determine the discount factor function. I get the data for Coupons, Face Values and Closing Prices from Thomson Reuters, which I insert into the Dataframe ...
0
votes
0answers
5 views

Complex yields occur for some sets of cash flows

My question is not inherently related to Matlab but if there is a solution using Matlab that would be great. I have inherited some Matlab code that uses the function bndyield to get the yield of some ...
0
votes
0answers
4 views

Estimating $\mu$ - only increasing $T$ improves estimate?

Assuming an asset price $S$ follows a geometric Brownian motion (GBM), the log returns $R$ are distributed as $$ R_i := \log\left(\frac{S_i}{S_{i-1}}\right) \sim \mathcal{N}\left(\left(\mu - ...
0
votes
0answers
9 views

How to adapt a Moving Average period to market conditions?

I would like to know if there is some way to adapt the period of a moving average to market conditions like for instance the stop loss can be adapted to market conditions using the average true range. ...
8
votes
1answer
341 views

Consistency of economic scenarios in nested stochastics simulation

I am interested in references on research regarding the consistency of economic scenarios in nested stochastics for risk measurement. Background: Pricing by Monte-Carlo: For pricing complex ...
5
votes
1answer
111 views

Time value of option not always leading to an increased option value

My understanding was that as you increase the time to expiry of an option, the value of the option increases. However, I have run a bunch of scenarios and have realized that if you assume a dividend ...
0
votes
1answer
33 views

Examples using PyOpenCL for backtesting trading strategies? [on hold]

Anyone used PyOpenCL for backtesting trading strategies? Any qualitative/quantitative benchmarks of implementations in Python, Cython, PyOpenCl? Is it worth it spending time implementing extra Lines ...
3
votes
0answers
28 views

GARCH model, expectation of volatility?

Consider a time series $\{r_t\}$ following a standard GARCH(1,1) model, i.e., $$ r_t = \sigma_t \epsilon_t,$$ where $\epsilon_t \sim N(0,1)$ and are i.i.d, and $$\sigma_t^2 = \omega + \alpha_1 ...
4
votes
1answer
88 views

Getting ETF data from google finance

I hope this is on-topic. I want to set-up a set of investment rules and back-test it on a mix of asset-classes. Thus I thought that using ETFs for the back-test would be a good idea (time series could ...
3
votes
1answer
24 views

Annualised Sharpe Ratio for Index vs Index Benchmarking

I am currently writing a paper about the performance characteristics of alternative energy equity indexes and am therefore comparing them to their benchmark indexes (msci world, etc). To calculate the ...
1
vote
2answers
50 views

How to get Stock Fundamental time series data?

I need key Stock Fundamentals like in http://finance.yahoo.com/q/ks?s=KO+Key+Statistics But that page shows only the last quarter data, I need to analyze how that data has changed over past years. ...
-1
votes
0answers
23 views

Estimate total variable cost function (TVC) and average variable cost function (AVP) from marginal cost function (MC) [on hold]

I need to estimate the function expressions for $TVC$ and $AVC$ from the $MC$ function for different amounts of quantity $(Q)$ From the solutions I have, that For $Q \leq 50$ $MC1(Q) = -Q + 100$ ...
0
votes
1answer
9 views

convert three months interbank rate into monthly rate

I have a time series of the three month interbank rate each month and I suppose that the rate is has yearly frequency. I need these interbank rates to be on a monthly basis because I want to us these ...
1
vote
0answers
40 views

Orderbook Arbitrage

The orderbook of trading exchanges are nowadays mostly hidden as so-called "Dark Pools". The measure was taken to avoid various market manipulation strategies which were apparently executed by traders ...
1
vote
0answers
21 views

PDE vs TREE vs MC vs Analytical

One what basis the pricing model can be differentiated for particular trade pricing. For exapmle why PDE or Binomial tree or MC or Analytical method will be consider for pricing any trade. Question ...
3
votes
0answers
18 views

Quantitative Real Estate Investment Finance

I'm wondering if there is an application of quantitative finance to real estate investment? Specifically I'm wondering about models for pricing small neighborhoods (or even single houses) that take ...
1
vote
0answers
17 views

Recording Google/yahoo finance data streams

Is there any way to record or piggyback with an app, code or excell goggle finances' (or yahoo even) data stream? Ideally i need tick by tick data, as in every price change of the day. All the ...
2
votes
3answers
61 views

Multi-asset class allocation

How to allocate asset classes in a multi-asset portfolio? An institutional client needs to meet his pension liabilities, and suggested a multi-asset-class strategy. I'm trying to find ideas to pitch. ...
3
votes
0answers
22 views

how we can derive $PIDE$ of double exponential Jump-diffusion model (we know as kou model)?

I'm working in double exponential Jump-diffusion model (we know as kou model) with following form , under the physical probability measure $P$: \begin{equation} ‎\frac{ds(t)}{s(t-)}=\mu‎‏ ‎dt+\sigma ...
0
votes
1answer
89 views

Gamma derivation from the expectation

I am trying to derive Gamma from the expectation principle (differentiating under expectation sign). I understand these steps $\frac{d^2 C}{d x^2} = e^{-r\tau} \mathbb{E} [ \frac{\partial}{\partial ...
4
votes
1answer
1k views

Historical volatility from close prices (Haug pg 166)

I have implemented a function for calculating historical volatility using close the close method as described by Haug on page 166. When I implemented the formula given by Haug, it resulted in some ...
3
votes
3answers
689 views

Two different ways of pricing that leads to two answers

This question might appear trivial to many (considering the questions on this site), but I think it reflects something fundamental that I am missing. To keep things simple, assume everyone is ...
1
vote
1answer
45 views

How to use Halton sequence in monte carlo simulation

Does anybody know how to use the Halton pseudo random technique in monte carlo simulation. I'm able to generate the sequences and I know they are correct. I checked a couple of numbers from different ...
0
votes
0answers
13 views

Perpetuity Time Value of Money Question [on hold]

trying to learn finance on my own here. Here's the question: DPC Corp. currently pays a dividend of $2 per share and the dividend is expected to grow at a 0 percent annual rate for three years, then ...
4
votes
2answers
89 views

Beta between stock and option

In Black Scholes model I would like to compute $$ \beta_K = \frac{\mathrm{cov}(C_{K,T},S_T)}{\mathrm{cov}(S_T,S_T)} = \frac{\mathrm{cov}((S_T - K)^+,S_T)}{\mathrm{cov}(S_T,S_T)} $$ with respect to say ...
3
votes
2answers
71 views

Do futures follow physical or risk-neutral distributions

I've spent a while looking for an answer to this question and while I feel it is a simple question I have not found an answer. I know prices of option contracts follow an implied, risk-neutral ...
3
votes
2answers
42 views

Joint probability distribution only measures product sets?

According to these notes (top of p 133), "We say that random variables $X_1, X_2, \ldots X_n : \Omega \to \mathbb{R}$ are jointly continuous if there is a joint probability density function $p(x_1, ...
-6
votes
0answers
33 views

What's the best proffesional forex market data feed out there?

I trade Forex latency arbitrages and find it harder and harder to get a reliable New York market data feed to serve my purpose. Reuters and EBS send timesliced updates every 500ms for 5k/month which ...
2
votes
1answer
32 views

Matlab Portfolio Optimization with bid ask spread

I'm trying to find the optimal portfolio of options and stock which minimizes the standard deviation of the portfolio returns but also taking into consideration the bid and ask prices of the assets. ...
2
votes
1answer
50 views

VaR calculation methods of options

I am a little bit confused about VaR in Options and I need a clarification for. I collected the following formulas, can you suggest what is the best formula and explain me why, please?
0
votes
1answer
27 views

Diebold-Mariano test

I am trying to use the Diebold-Mariano test but it doesnt work for some reason. Here is my code: dm.test(maegarch14,maeegarch14,h=126) where ...
11
votes
2answers
1k views

Is there a popular curve fitting formula of options skew vs strike price or vs Delta?

I was trying to build a options trading/optimization system. But it often gets more inaccurate as it scans through the far from ATM options because, you know, options skews. That is because I did ...
3
votes
2answers
67 views

Time 0 value of an American Put in Cox-Ross-Rubinstein model

This is a question from a problem sheet which I have handed in and have solutions for. The only examples of this in class I have seen are examples where the interest rate is 0. "Consider a ...
0
votes
1answer
19 views

Extracting Default probability from a single CDS

I have to find the CDS's default probability using the simplest Poisson Process (intensity constant). I'm wondering how to get this estimate if I have only a CDS with maturity 5years. If I had ...
2
votes
1answer
47 views

Measure the effect of a natural disaster on a stock market index

I am very new to using stata and very new to using Garch models. I am currently doing my final dissertation for my MSc in Finance studies and regarding my topic I understood that i had to use garch to ...
1
vote
1answer
50 views

Estimating correlation using EWMA

I am using an EWMA model to evaluate the correlation between yearly time series. I know Riskmetrics uses $\lambda=0.94$ for daily data and $\lambda=0.97$ for monthly data. Is there a value ...
3
votes
1answer
76 views

Is there a countably infinite Sigma-Algebra? Why?

Assume $\,\mathcal{F}$ be a nonempty collection of subsets of $\Omega$. $\,\mathcal{F}$ is called a $\sigma$-Algebra whenever if $A\in\mathcal{F}$ then $A^c\in\mathcal{F}$, and if ...
1
vote
1answer
173 views

How to projectP&L or drawdowns on pair trading , trading and portfolios? [on hold]

This is for planning and risk management. I am stuck on the following thoughts - Back-test the trading strategy for a period similar to the one you expect and then project. Do the above using ...
3
votes
2answers
35 views

Implied volatility and nonconstant volatility

John Hull states in his text that "AS the maturity of the option is increases the percentage impact of nonconstant volatility on (option) prices becomes more pronounced, but its percentage impact on ...
5
votes
1answer
363 views

Definition of risk factors for market risk scenario testing

I am doing a research for stress testing in market risk. The usual process I found out for scenario testing is: Define risk factors upon the portfolio Define the desired scenarios Vary the risk ...
1
vote
1answer
61 views

Bond in relation to US T-Bill/Risk-Free rate

By looking at the following charts , i wondered about how to plot a fixed income security against a risk free bond. I have the bond price time series but I am not sure what US T-Bill rate I should ...
2
votes
1answer
41 views

Applying Time Delay Neural Network to financial events

I have an IT background and I would like to use data from a forex calendar like this one to predict prices. The problem is that calendar news impacts can last for days or weeks or even can effect ...
2
votes
1answer
15 views

Forced to exercise gap options

I was reading a textbook and came across some surprising stuff in the section about gap options. Let $X$ be a payoff function such that $X=\Big\{\matrix{0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...
2
votes
0answers
77 views

Problem with Naive Bootstrapping (US Government Bonds)

I am using the formula here to determine the discount factor function and eventually the zero-coupon yields. I get the data for Coupons, Face Values and Closing Prices from Thomson Reuters, which I ...
4
votes
1answer
142 views

Kolmogorov-Smirnov test for Generalized Pareto Distribution

I've fitted my data to a generalized pareto distribution as to model the returns in the tails more accurately. The interior is fitted with kernel distributions. I would like to now test whether the ...
3
votes
2answers
168 views

IR Yield Curve and Fixing Dates

Consider two FRAs. 3x6 , Effective 3 months from now, terminates in 6 months. The floating leg payer pays 3-month LIBOR. Fixing date for LIBOR 40 business days. To price this at par, the fixed leg ...
0
votes
1answer
49 views

Do I need simulink to model the risks of an option portfolio

I wish to buy Matlab Home and learn to model the risks of a derivatives portfolio and then stress test it. So I am guessing I will need : Stochastic calculus Linear algebra Stats/Probability Some ML ...
3
votes
1answer
94 views

Heston Model Option Price Formula

What is the formula for the vanilla option (Call/Put) price in the Heston model? I only found the bi-variate system of stochastic differential equations of Heston model but no expression for the ...
-1
votes
0answers
17 views

What is the advantage and disadvantage of using moving average crossover stratergies for algorithm trading [on hold]

I am new to algo trading and the first algorithm I learned is moving average crossover. I find this algorithm more easy to learn and implement but when I back-tested this strategy with different time ...

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