1
vote
1answer
33 views

Question regarding sinking fund

I am currently studying about financial mathematics for my Exam FM to become an actuary. There is one thing that really bothers me so I would like to have some answers. Whenever I solve a problem ...
1
vote
0answers
59 views

How to apply the chain rule for partial derivatives to transformations?

I'm currently working to solve the Black-Scholes model partial differential equation (it's a model for a.o. stock option prices). The Black-Scholes equation for a calloption C(S,t) is given by $ ...
2
votes
1answer
261 views

What is Margin of Conservatism

In modelling loss given default,(LGD), we often encounter the term Margin of Conservatism. What is it in layman's terms? I am not able to find a wikipedia page on this.
1
vote
2answers
337 views

How can I create a public viewable stock market index?

I have 3,000 tickers that I would like to turn into a weighted index, viewable by the general public by going to Yahoo and typing in ^PSNDX (for example) or go to E-Trade and enter something similar. ...
1
vote
1answer
250 views

Get distribution for aggregate loss using Monte Carlo

I am given two data sets containing dates and losses (in some currency). Given a distribution for the amount of losses and an (a,b,0) distribution for frequency of losses, how can I use Monte Carlo ...
1
vote
1answer
31 views

Spread options on prices or returns?

I need some clarifications regarding spread options. I have always found them characterized as paying, at maturity, the difference between the prices of two underlying assets: $$ (S_1(T)-S_2(T)-K)^+ ...
4
votes
0answers
53 views

What kind of errors arise when I fit ARMA(1,1) to data generated from ARMA(1,1)-GARCH(1,1) process?

As far as I know estimates of parameters of ARMA(1,1) are asymptotically optimal when fitted to data from ARMA(1,1)-GARCH(1,1) process, and only their variance increase, so when we assume large ...
2
votes
0answers
39 views

Portfolio optimised for diversification and regular yield. How to hedge?

Here is a portfolio optimisation for equity dividend and yield designed to diversify holdings and produce regular monthly returns using only ETFs complete with R code. ...
1
vote
1answer
60 views

Can wavelets be effectively used to approximate the market value of an illiquid instrument?

Considering less liquid instruments can have a higher degree of volatility especially on lower time frames (1-tick or 1-second), is it possible to effectively use wavelets to reduce the issue of noise ...
3
votes
1answer
237 views

Portfolio choice problem of a CARA investor with n risky assets

Ok, I am working on a problem that consists of the following: I am looking to solve the portfolio choice optimization problem (maximizing utility with a known utility function) in the case where all ...
1
vote
0answers
47 views

Comparing cost of two alternative given their distribution

I have distribution for cost of two alternative through Monte Carlo simulation. The distributions are not normal. Given the benefit of the two alternatives is the same but ungiven, I want to choose ...
3
votes
1answer
458 views

Covariance matrix and Cholesky decomposition

I am simulating a spread option with stochastic volatility using Monte Carlo simulation. I have the positive-definite covariance matrix $$ \rho = \left( \begin{array}{cccc} 1 & \rho_{1,2} & ...
3
votes
1answer
216 views

Constant Relative Risk Aversion

The question: Consider a person with constant relative risk aversion p. (a) Suppose the person has wealth of 100,000 and faces a gamble in which he wins or loses x with equal probabilities. ...
1
vote
1answer
68 views

Foreign exchange - Dealer spreads and order size

Is it true that in foreign exchange markets, dealer spreads are lower for smaller order and increases for larger orders? This seems counter-intuitive when compared to other markets where dealer ...
2
votes
1answer
574 views

Calculate spread for pairs trading

What is the best way to begin calculations for pairs trading? I have seen two ways: 1) Start from the price ratio (StockAPrice/StockBPrice) and calculate mean, standard deviation and z-score from a ...
1
vote
1answer
75 views

On a source for a mean-variance portfolio optimization result

In the context of a mean_variance framework consider an optimizing investor who chooses at time $T$ portfolio weights $w$ so as to maximize the quadratic objective function: $$U(w) = E[R_p] - ...
0
votes
1answer
113 views

how to make a nonlinear gird where grid points are not equally spaced?

I need to make a grid [0,1] with points that are concentrated close to the edges (close to 0 and 1) while the remaining points in the middle can be equally spaced. The reason for doing this is that I ...
2
votes
2answers
98 views

Q regarding amortization of 500,000 loans

I am brand new to this forum. I asked this question on the main StackOverflow site and it was suggested that I ask here. My task is to find a method to quickly calculate the monthly cash flow on ...
3
votes
2answers
171 views

How to get around flat likelihood function when calibrating GBM parameters?

I want to calibrate jointly the drift mu and volatility sigma of a geometric brownian motion, $$\log(S_t) = \log(S_{t-1}) + (\mu - 0.5*\sigma^2) \Delta t + \sigma*\sqrt{\Delta t}*Z_t$$ where $Z_t$ ...
0
votes
1answer
102 views

Bivariate Black-Sholes Model

Let us propose bivariate Black-Sholes Model. Assume, we have an arbitrage-free complete market. $r_{f}$ is risk-free rate. Under real-world measure $P$: $dS_{1} (t)=S_{1} (t) ...
5
votes
2answers
246 views

Impact on bid/offer due to volume/size of trades placed

When observing bid/offer in the market I came across a question. How much trading a bond would impact its spread for subsequent trades ie. what is the impact on bid/offer due to volume/size of ...
1
vote
1answer
32 views

convention in borrowing money in a multiperiod model

I have a question concerning the idea of consumption in multi period. The following is given $$C_1=W_0-xS_1+B$$ $$C_2=xS_2-BR$$ where $W_0$ is initial wealth $x$ is the weight on an asset with ...
1
vote
1answer
181 views

Why model the variance-covariance matrix as an inverse-Wishart distribution in bayesian portfolio analysis?

I am following Risk and asset allocation (Attilio Meucci,2007). I must say I am enjoying this reading quite a lot so I hope nobody takes my question as a critique on the text. When we are introduced ...
1
vote
0answers
56 views

Interpretation of Correlation Matrix

I have past data which is in vector form. The information shows the probabilities of a AAA rated company to migrate to another credit rating. So for example, (x1, x2, x3) has the probabilities of ...
1
vote
0answers
60 views

Convolution of inverse gaussian and power law distributions

I am trying to understand how the first passage time density of Brownian motion with drift is modified by the presence of waiting times that are distributed as a power law In other words, what is the ...
2
votes
2answers
245 views

Why do we need $dS_t=r S_tdt+\sigma S_tdW_t^Q$?

Suppose $S_t$ is the stock price and follows the dynamics $$dS_t=\mu S_tdt+\sigma S_tdW_t$$. According to Girsanov, we can apply change of measure and obtain $dS_t=r S_tdt+\sigma S_tdW_t^Q$, this ...
0
votes
2answers
247 views

How to price exotic options using Monte-Carlo?

I am actually trying to solve some exercise problem using Monte-Carlo and C++ for exotic options. Namely, the exotic options are geometric Asian options and discrete barrier option. It is claimed ...
1
vote
1answer
99 views

European vanilla call/put option, when volatility increases, how will gamma changes?

according to the BS formula, $\gamma = \frac{N'(d_1)}{S_0\sigma\sqrt{T}}$, gamma will decrease when volatility increase. How does it intuitively make sense? rather than from the formula.
1
vote
0answers
67 views

Straddle neutral strategy

What does it mean to implement a delta-neutral strategy for straddle ? A straddle consists in buying a call and a put simultaneously, at the same date, on same underlying, with same maturity and ...
3
votes
2answers
92 views

arbitrage opportunity in a two period model

I have a little problem evaluating an european call. I Suppose the following: in $$t=0 : S_0 = 10$$ $$t = 1 : S_1 = \{10,11\}~with ~p=0.5$$ riskless rate : $(1+r)=\beta=1.049$ Strike ...
3
votes
0answers
200 views

Constructing Volatility Smile from American Options

My question is about best practices for reconstructing volatility smiles for a fixed tenor from American option data. For simplicity/liquidity, I am currently considering options on SPY. I am ...
1
vote
2answers
56 views

Cheapness indicator for Convertibles Bonds

What indicator (or combination of those) could be used to roughly estimate the cheapness of a convertible bonds ? Like the price/earning ratio for equities. Thanks, Max.
1
vote
1answer
258 views

SEC 13F Security List has incorrect CUSIP numbers?

I'm building database of 13F sec.gov forms with 13F security lists (http://www.sec.gov/divisions/investment/13flists.htm). Along with integrity checks. I implemented CUSIP digit check algorithm to ...
1
vote
1answer
99 views

Where to obtain Eurex level 2 historical order book data from?

What are some possible sources to obtain Eurex level 2 historical order book data from? Unfortunately I have only been able to find 1 source - namely Eurex itself, which charges 2000 Euro/month for ...
1
vote
1answer
491 views

Bloomberg equity option volatility data

Using the Bloomberg open API, I am trying to program a C++ script that is able to download option volatility data from Bloomberg. I currently do not have access to Bloomberg, but in the coming week I ...
1
vote
1answer
237 views

Which sports are generally the best for trading on betting exchanges for a profit?

I am looking at trading bets on tennis, football and horse racing in particular as these appear to have the most liquidity. How much background research and how much trial and error is generally ...
4
votes
1answer
106 views

Black-Scholes: If exercise probability is 0.5, should $D_2$=0?

Let's say we have option strike price equal to current stock price. And we have zero risk-free rate. In this case I assume that probability of exercise is 0.5 because chances that price will go up or ...
0
votes
0answers
24 views

VIX For Convertible Bonds

Is there something similar to the VIX but related to the convertibles bonds market in the U.S. ? Thanks, Max.
2
votes
0answers
115 views

Why random walk Metropolis Hasting algorithm works bad on GARCH(1,1) parameters estimation

I am trying to estimate the parameters of the GARCH(1,1) model with MCMC method, firstly, I read the paper: http://mpra.ub.uni-muenchen.de/12985/1/MPRA_paper_12985.pdf Metropolis Hasting method is ...
3
votes
0answers
58 views

Dixit & Pindyck (1993) Chapter 4, equation 13

Starting with the Bellman equation for the optimal stopping problem: $$F(x,t)=max\{\Omega(x,t), \pi(x,t)+(1+\rho dt)^{-1} E[F(x+dx, t+dt)|x]\}$$ In the continuation region where the second term is the ...
2
votes
1answer
130 views

Volatility Surface Constituents, do's and dont's

Recently I have been working a lot with implied volatility and volatility surfaces. The basic idea is easy to follow: 1) Gather market prices of options at different (Strike,Expiry) 2) Calculate ...
1
vote
2answers
344 views

Why is the vega of an at the money option so insensitive to movements in volatility? I.e, why do ATM options have such little Vomma?

I've been trying to understand why at the money options have very little vomma. I was reading and came across a graph that showed vega as volatility changes and I couldn't grasp how the relationships ...
5
votes
1answer
131 views

Which volatility to use to price options on futures contract?

I have some questions regarding pricing futures options and I just want to be sure that my thoughts are correct. I am trying to price options on futures for american & european style. In the ...
0
votes
1answer
67 views

Effective & Maturity Date Modified Following

I am constructing discount curve for tenor 1 month. First Instrument - PLN_1M_WIBOR has Effective Date on 2015-01-29 (spot). I was wondering what Maturity Date should be? 2015-02-27 or 2015-03-02? I ...
4
votes
3answers
234 views

On learning the bayesian approach to portfolio optimization

I am required by my course to write a small paper on the Bayesian approach to portfolio optimization, I am following Applied statistical decision theory [by] Raiffa, Howard. Which can be consulted ...
3
votes
2answers
253 views

Black-Litterman: Why should the views be independent of each other?

This question relates to this question. In the Black-Litterman framework views of inverstors on the market are modelled. These views have a covariance-matrix $\Omega$. I always found it quite ...
0
votes
1answer
343 views

What constitutes an “odd lot” in corporate bonds trades?

This is important in price discovery and pricing of bonds based on trades. "Odd" lots are traded at lower prices than "round" lots. However I wasn't able to find a definition of "odd" lot anywhere. ...
1
vote
3answers
486 views

Is the CAPM beta equivalent to the coefficient estimate of an OLS regression?

The $\beta_i$ of an asset or portfolio is defined as its covariance with the market (which itself therefore has a beta of $\beta_m = 1$). The CAPM looks a lot like a simple linear regression model. Is ...
1
vote
0answers
61 views

Convertible bonds market data

My question is twofold. First, what are the key informations used to describe a convertible bond market ? I'm thinking about market size, conversion rate, appropriate index, ... Second, where to ...
-2
votes
1answer
61 views

Magrabe Exchange Option: not equal drifts

I need to calculate the price of exchange option between 2 assets $S_1$ and $S_2$ The formula is given here Wiki: Magrabe formula or here Quant Stack Exchange. In the derivation of the formula it is ...

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