2
votes
1answer
75 views

Martingale Measure for Vasicek process

First, under Black-Scholes we have the usual method to transform the discounted asset price into a martingle: Let the asset price $S_t$ be goverend by $$ dS_t = \mu S_t dt + \sigma S_t dW_t, $$ so ...
2
votes
1answer
39 views

How is the Order priority of an Iceberg order decided?

Typically, markets guarantee a FIFO order of priority of execution for various orders at the same price. I want to know does this hold true for Iceberg orders? for eg Order1 = Buy 100 Quantities @ 2 ...
1
vote
1answer
89 views

Pricing call option

Question: The price of a stock is 100. With equal probabilities, it either goes up to 130 or down to 70. What is the price of a 1 year call option with exercise price 100. Risk free rate is 5%. ...
0
votes
1answer
66 views

Volume or Volatility?

I've recently been given a project which came with some documentation. In this documentation is a bullet point that reads: Liquidity Risk in Equity, Credit and Vol I'm unsure as to whether vol is ...
1
vote
0answers
23 views

Why is TransactTime not required on ExecutionReports? [closed]

A couple of my brokers are not sending tag 60(TransactTime) on Canceled messages. What is the rule of thumb for determining cancel time when tag 60 is absent from a Canceled message? Canceled ...
1
vote
0answers
55 views

B-S Put Option Formula: Derivation using expected value under Q

I have been working on an old problem in one of my finance classes and, since no solution has been provided and I won't be able to contact my teacher anytime soon, I was hoping I could ask you guys to ...
0
votes
0answers
43 views

Regressing NYSE returns: Lagged intercept term & efficient market hypothesis

By performing the following OLS time series regression, $y_t$ = $\beta_0$ + $\beta_1$*$y_{t-1}$ + $\beta_0$*$y_{t-1}^2$ + $\epsilon$ I cannot reject the null hypothesis that b1=b2=0. However, ...
0
votes
0answers
57 views

Cointegration and variance of time series

Given that $X_t , Y_t$ are two cointegrated random processes, what can we say about the relationship between variance of the two increments $var(X_{t+h}-X_t)$ , $var(Y_{t+h}-Y_t)$ for a given ...
2
votes
1answer
49 views

Systematic Views in Black-Litterman?

Are there any literature on selecting systematic views for Black-Litterman along with methods to specify the uncertainty parameter? For example, rather than specifying a portfolio manager's subective ...
2
votes
2answers
88 views

Forex trading scenarios - calculating units

I'm trying to build an automated forex trading system and I'm trying to understand how to calculate the number of units I should specify for each trade in different scenarios. Say for example I have ...
2
votes
1answer
124 views

S&P 500 total return since 1956

I'm looking for monthly data of the S&P 500 total return since 1956. I have looked into Bloomberg and Datastream, but it looks like there are data only from 1988.
0
votes
2answers
62 views

Short Volatility [closed]

Being net short options is an obvious case of being short volatility. But what other investments are "functionally" short volatility? Is long equities long or short volatility? Is short Apple long or ...
1
vote
1answer
34 views

Portfolio Selection formulation

I was just wondering why in http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1601412 on page 22, the constraint (48) is a strict equality for the minimum variance formulation. Whereas in a different ...
2
votes
1answer
138 views

Why is the volatility smile important

One thing I can't understand clearly is why there is so much focus on the volatility smile. Given my knowledge of the Black and Scholes model, this is what I get: People use the volatility smile as a ...
1
vote
3answers
122 views

Direct use of implied volatility

I am not sure to understand exactly the direct use of implied volatility. Let's take an example: if an instrument has a daily volatility of $\sigma$, there is a 68% probability that its value will be ...
1
vote
1answer
53 views

remove seasonality in future contracts

very new to commodities. I have raw agriculture future data, and I need to remove the seasonality (de-seasonalize) from the data, what is the general approach ? Thanks for the help!
1
vote
2answers
39 views

When would dedicated portfolios do better than 'immunized' portfolios?

We just learned about cash-matching through dedicated portfolios (using risk free bonds) in my class that concerned mathematical programming. However, in an aside one of the notes said: It should be ...
0
votes
2answers
50 views

Calculating units in a cross currency short trade

If I have a forex account with a broker and a balance of 100 USD, and I'd like to short EUR/JPY, how many units can I short? How is this calculated? Which currency pair do I use to translate between ...
1
vote
0answers
69 views

Black Scholes Model Replicating Strategy Delta Hedged Exam Question

A share is currently priced at 640p. A writer of 100,000 units of a one year European put option with an exercise price of 630p has delta-hedged the option with a portfolio which holds cash and is ...
2
votes
1answer
66 views

Pricing digital options in discrete time

I am stuck in this exercise from my textbook: Consider a one-period market model with $N+1$ assets: a bond, a stock and $N-1$ call options. The prices of the bond are $B_0=1$ and $B_1 = 1+r$, ...
1
vote
2answers
136 views

Intuitive Reasoning for Using Risk-Neutral Measure

Although we thoroughly covered risk-neutral pricing in university I never fully understood it in the context of continuous-time processes. But first of all, lets consider a discrete time example: ...
2
votes
1answer
49 views

How to measure the performance of an systematic option strategy

I have a strategy based only on option instruments and I am trying to measure its performance to optimize some parameters. But how does one measure the performance of such strategies? For Sharpe ...
0
votes
0answers
38 views

Term Structure and short rates

If I have a term structure/yield curve given by: $$f(t, T) = f(0, T) + σ^2t(T − \frac{t}{2}) + σB_t $$ and want to find the short/spot rate $r_t$, is this simply: $$f(t,t) = f(0,t) + ...
2
votes
1answer
85 views

stochastic calculus - brownian motion

I don't know how to prove this : let be $X_t = \int_{0}^{t}\sigma_{u}dW_{u}$ where $\sigma_{t}$ is a predictable process. If $|\sigma_{t}| = c$ a.s. how can I prove that $X_{t}=c*\beta_{t}$ ...
1
vote
0answers
15 views

Calculation of bond spot rates [closed]

the cash prices of six months and one year treasury bills are \$120 and \$115 respectively. A 1.5 years bond that will pay coupons of \$5 every six months currently sells for \$121. A 2 years bond ...
1
vote
2answers
94 views

Buying OTM puts and then selling stock

What is to stop someone from first buying a bunch of OTM puts and then selling short enough stock to make the puts go up high enough to make a profit? Or conversely, buying OTM calls and then buying a ...
1
vote
1answer
53 views

parameters in Heston model and their impact on volatility smile

Consider the Heston model given by the following set of stochastic differential equations: $$\frac{dS_{t}}{S_{t}}=\mu_{t}dt+\sqrt{V_{t}}dW_{t}, S_{0}>0,$$ ...
2
votes
1answer
36 views

How to deal with missing returns when creating value (equal) weighted returns

recently I am doing cross sectional regressions, and getting confused about missing returns. Suppose we have 100 stocks, then we want to construct a value weighted return (or equal weighted return). ...
1
vote
1answer
100 views

stochastic calculus - Itô formula?

I encounter a problem in the proof below: I don't know how to proove the first line in yellow (cf below): it makes me think about the Itô formula a lot I don't undertand the deduction (ok ...
3
votes
2answers
153 views

What are the main market anomalies/inefficiencies detected in quantitative finance?

I wondered about the existence of a complete list of the anomalies detected in quantitative finance. Generally, a market anomaly or inefficiency is a asset price and/or rate of return distortion on a ...
3
votes
0answers
36 views

How to price lookback american option when its payment is distributed during its life

I would like to price a floating strike american lookback with a particular feature: I don't want to charge upfront the client, rather I would like to insert a "running fee", some sort of a dividend. ...
1
vote
1answer
45 views

equality in distribution

I encounter the following problem : I have the equality in distribution: for all $\lambda >0, ((1/\lambda)*\int_{0}^{\lambda t}\sigma_{u}^{2}du,t\geq0)=(\int_{0}^{t}\sigma_{u}^{2}du,t\geq0)$ ...
0
votes
1answer
72 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 ...
1
vote
1answer
65 views

Delta derivation from the expectation

I'm trying to understand the following transformation leading to Delta $\frac{dC}{dx} = e^{-r\tau} \mathbb{E}[ \frac{\partial}{\partial x}\text{max}(xY-K,0)] = e^{-r\tau} \mathbb{E}[Y ...
2
votes
0answers
67 views

Modeling market sentiment and pricing options by volume, open interest

Are there any empirically-proven methods/formulas for weighting IV surfaces, pricing a discount/premium in an option, and/or adjusting any of the 1st- or 2nd-order Greeks for the magnitude (volume or ...
2
votes
0answers
44 views

Comprehensive List of Regime Switching/ Change Point Models

I am looking for a comprehensive list of regime switching/change point models/techniques which can be used to model different regimes / change points in financial time series. What I found so far are: ...
1
vote
1answer
44 views

Relationshiop between central bank official currency rates and spot forex

Central banks publish official figures for domestic interest rates, as well as spot currency rates for a few select countries (largest trading partners). To prevent arbitrage, I "expect" that in the ...
1
vote
1answer
41 views

forward option, stochastic calculus

I encounter a problem to understand this: The price of a forward option is : $C(K,t,T)=\mathbb{E}[((S_{T}/S_{t})-K)+]$ OK The option should only depend on $T-t$ because the yield randomness (for a ...
1
vote
1answer
45 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
0answers
74 views

Modified duration in multi-currency portfolio

I was thinking about how to figure aut duration for portfolio of bonds denominated in different currencies… I would like to compare sensitivity of portfolio to shift of yield with competitive ...
3
votes
3answers
147 views

References on Statistical Arbitrages

Is there any basic materials (books, papers) to read on Statistical Arbitrage? I certainly understand much of the useful information is in the industry. I just want to get some understanding on the ...
4
votes
1answer
212 views

Moving window forecasting in Python

I am looking to create some code that will out-of-sample forecast the HAR-RV model. The model itself is formulated as the following, and the betas are estimated through HAC-OLS or Newey-West. ...
7
votes
2answers
124 views

American Call: when it's European?

It is a rather well-spread fact that in Black-Scholes (BS) model for a stock with no dividends that follows Geometric Brownian Motion (GBM), the price of American call coincides with that of its ...
2
votes
1answer
44 views

martingale decomposition problem

Let $G_{t}$ be a filtration and $M_{t}$ a $G_{t}$-martingale. Why do we have this decomposition: $H_{t}=\mathbb{E}[H|G_t]=\int_{0}^{t}h_{s}dM_{s}+R_{t}$ where $R_{t}$ is a martingale orthogonal with M ...
2
votes
2answers
104 views

Stochastic Differentials - Ito's formula for a self-financing portfolio

Suppose I have a portfolio of stocks $(S)$ and savings account ($\beta_t$) then, the value is $$V = a_t S_t + b_t \beta_t$$ and for this portfolio to be self replicating, we need by Ito's lemma $$dV ...
2
votes
1answer
54 views

Solving a Non-Linear PDE using a Finite Difference Scheme

I have the following non-linear PDE and I have no idea how to go about solving it using a finite difference scheme in Python. Can someone get me started and/or point me to an algorithm for doing this? ...
2
votes
0answers
55 views

Pricing a zero with Vasicek model

I'm trying to understand bond pricing with the Vasicek interest rate model. I'm using McDonald's book for this purpose (not homework). Recall that Vasicek dynamics are \begin{equation*} ...
0
votes
0answers
18 views

Pricing formulas for affine stochastic volatility jump-diffusion models

Does anyone know a reference where I can find the pricing formulas for vanilla calls in the affine stochastic volatility jump diffusion class of models such as SVJ and SVJJ? I am looking for ...
0
votes
0answers
16 views

Value of sequential mutually-exclusive options (A variant on the Secretary Problem)

How much should you offer a potential hire in a signing bonus? Imagine you are interviewing a list of candidates for a particular job. Each candidate has a "lifetime value", and probability of ...
0
votes
0answers
27 views

FX rollover swaps rates based on LIBOR rates

I am trying to calculate FX swaps overnight rates based on LIBOR rates Example: Libor rate for TRY crosses is 12.00 Libor rate for USD crosses is .19 How do we get to these number? USDTRY swaps ...

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