All Questions

1
vote
1answer
32 views

Calculating Ex-ante Sharpe Ratio in multi-period setting

I have built a return process $\{x_t, t = 1,\dots,T\}$ for an asset. Suppose I have generated $K$ sample paths $\{x_t^j, t=1,\dots,T\}, j=1,\dots,K$. I think of two ways to compute the Sharpe ratio. ...
3
votes
2answers
78 views

Predicting portfolio returns

I suppose there are roughly two approaches to predict portfolio returns. Either predict the returns of all underlying stocks and aggregate all individual stock predictions, or predict the portfolio ...
1
vote
0answers
29 views

Using CFNAI index for identifying sample periods

I'm doing my Thesis on Asset pricing models and I would like to find out the effects of business cycles on the performance of asset pricing models for industry portfolios. My initial idea was to ...
0
votes
1answer
54 views

How much senior debt could be issued? [closed]

Is there a limit on how much senior debt could be issued? If a company issues a small amount of debt relative to its assets and wants to issue more could it still be called "senior" or it would have ...
3
votes
2answers
98 views

Find the brownian motion associated to a linear combination of dependant brownian motions

I have $N$ correlated standard one-dimensional Brownian motions $W_1,\ldots,W_N$ with correlation matrix $\rho$ and I consider the process $Z_t \equiv \sum_{i=1}^N \mu_i (t) W_t$ where the $\mu_i$ are ...
0
votes
0answers
36 views

Using variance reduction on only some models

I am pricing options with some copula based models using Monte Carlo simulation. I was looking up some easily implementable variance reduction methods and decided on antithetic variates. However, ...
0
votes
0answers
48 views

Calibration of 1-factor Hull-White model using Jamshidians trick - see my code

So, I'm trying to calibrate the Hull-White 1-factor model given Black swaption volatilities that I have from the Bloomberg terminal. I'm following the Jamshidian method as described in this thesis (3....
1
vote
2answers
90 views

R: Book with extensive examples for either portfolio optimization or volatility forecasting?

I'm at a new job and there's the option to use R (you don't have to, but I'd like to). I used R years ago, so I while I'm somewhat familiar with it, I have forgotten most of it. For me, the best ...
0
votes
0answers
20 views

Where can I get large dataset [duplicate]

Where can I get large unbiased dataset for all stocks in the world (and not just the historical price but also the balance sheets fact and ratios). By unbiased I mainly mean to: 1. not being ...
0
votes
0answers
43 views

Brownian motion for modelling future asset values

Assume that an asset price $S$ is given by a Brownian motion. Argue from the definition why it is not possible to predict future values of the asset based on the past values of $S$. I am not sure ...
3
votes
1answer
71 views

Derivation and expectation interchange

I would like to know when it is allowed to interchange derivation and expectation. Suppose $X$ is some r.v whose dynamic is controlled by some parameter $\sigma$ and suppose $h$ is some smooth ...
2
votes
0answers
50 views

Bond spreads - SQASW

I posted this question in the finance/economics arm but someone suggested this would be a more relevant place. I have attached a photo of a list of bond issuance's in Australia. Could someone please ...
1
vote
1answer
58 views

Which are the practical implications that the continuously compounded rate of return can be smaller than the expected rate of return?

I'm reading Hull's Options, Futures and other Derivatives and it intrigues me that the distribution of the continuously compounded rate of return x is: $x \sim \phi(\mu - \frac{\sigma^2}{2}, \frac{\...
2
votes
1answer
65 views

Derivatives Trading Jargon

Could you please help to understand trading jargon in this tweet. Thanks in advance. For non twitter users: Bookie pushing 5-delta (strike of 8) 2 month TRY puts. 0.6%
0
votes
1answer
33 views

Is there any banking theory that can be confirmed or refuted? [on hold]

For example: There are many International relations theories. Depending on the object of study, the theory can be confirmed or refuted. I'm an intern in a bank. My responsibilities include data ...
0
votes
1answer
65 views

Should the sum of daily returns be close to monthly returns

I am calculating value-weighted returns with monthly dividends reinvested and for some reason when I sum the daily returns some are a little bit off with monthly returns. Is this normal?
2
votes
0answers
29 views

bond yield forecasting

About the problem of interest rate forecasting I find various paper that address the problem from the perspective of risk premia and affine term structure model. For example Cochrane and Piazzesi (...
3
votes
1answer
70 views

Solution to a Geometric Ornstein Uhlenbeck Process $dX_t = \kappa(\theta - X_t)dt + \sigma X_t dW_t$

I've been searching for the solution to the modified Ornstein-Uhlenbeck process \begin{equation*} dX_t = \kappa(\theta - X_t)dt + \sigma X_t dW_t \end{equation*} but it surprisingly hard to find. The ...
-1
votes
2answers
199 views
+50

Detect trend of an index

My question is about determining the trend and it can break down to 3 parts. To clarify, a trend in my point of view, and in simple form, is the last close at time t relative to its time reference, i....
4
votes
1answer
77 views

Is there a simple, intuitive derivation (using Taylor series) of the following approximation to Vega-weighted Implied Volatility?

The approximation is: $$\sigma \approx \frac{\sum V_j\sigma_j}{\sum V_j}$$ Background information from the first answer to this post: "Say that you have a portfolio of options with prices $P_j$. ...
1
vote
0answers
48 views

Duration and yield

I have some basic questions about mainly duration and yield. 1) Almost no-one defines what yield they are talking about when talking about duration and discount rate, I've seen some talk about ...
1
vote
0answers
30 views

Alternatives to implied or historical volatility for calculating implied correlation

For my thesis, I'm trying to calculate implied correlation values from bivariate options. I train my model on 10 years of returns data, price the options, and then invert Stulz's Formula (basically ...
1
vote
0answers
25 views

How to convert a vector of bonds ZC Spreads into default spreads

If we consider a set of bonds issued by a given entity that are quoted on the market, one can get for each of those bonds a ZC spread on top of reference swap curve (say the bonds are in USD and so we ...
2
votes
0answers
40 views

BSM PDE and diagonal dominance

I'm using the Thomas Algorithm to solve the Crank-Nicolson FD scheme. However, I've found that the matrix can occasionally fail to be diagonally dominant particularly when flat/local vol is very small....
2
votes
1answer
64 views

Deriving interest rate term structure in a short rate model

I have often seen a statement that we can model only a short rate process $r(t)$ and then use it to derive a term structure $R(t,T)$ for every $t$. Could someone please elaborate? Say, I’ve simulated $...
2
votes
0answers
28 views

Residual Risk and Variance

I've solved part a, but am struggling with b and c. $x_m$ is the market portfolio vector, and I think $T$ should be a diagonal matrix. Any hints greatly appreciated!
1
vote
1answer
48 views

Can anyone explain to how Hull get's from the stock returns to continuously compounded stock returns?

I'm reading Chapter 13 of Hull's book and am stuck on how he got from stock returns to continuously compounded stock returns. As a recap, he built the generalized Wiener Process, which describes a ...
1
vote
0answers
28 views

Proof of no arb condition after shifting SABR’s rho

Does anyone know of any paper or research where they shift SABR’s skew and rebuild the surface? In particular, I would like to prove theoretically whether the no arbitrage condition hold for the ...
1
vote
1answer
119 views

Mathematical models for personal finance decisions

I'm doing some bibliographic research on mathematical models for personal finance decisions. I should like to ask whether you know any of them, because the research that I did on Google Scholar haven'...
0
votes
0answers
20 views

Looking for a dataset with historical SP500 (100) components [duplicate]

Does anyone have a dataset of a complete list of the historical (starting from the 80s 90s something like that) composition of the SP500(100) with the dates when the tickers where removed from the ...
1
vote
0answers
31 views

Milstein discretization of the CIR process

Given the CIR process $\ dX_t = (a − bX_t ) dt + \sigma \sqrt{X_t}dW_t$ - I want to show that its Milstein scheme is $\ X_{i+1} - X_i = ((a − bX_i) - 0.25\sigma^2)\Delta + \sigma\sqrt{X_i}\sqrt{\...
2
votes
2answers
42 views

Are all changes of measures for continuous diffusion processes given by the change of drift?

In elementary discussions on change of measure for geometric Brownian motion, one often find statements like "change of measure = change of drift". Given a general continuous diffusion process of the ...
0
votes
1answer
59 views

Is there a straightforward way to get a “family tree” for a stock?

I would like to find a way to generate what might be called a "family tree" for a stock. Given a stock symbol and a future date, I'd like a graph (either literally or represented in list or other ...
1
vote
1answer
42 views

Can I calculate Sharpe ratio by running over many samples?

I have an algorithm that I am backtesting 200 times. It trades over 200 trading days per iteration. My sharpe ratio is calculated as follows: ...
1
vote
1answer
35 views

Efficient Frontier Graph

I'm writing some C code to create different portfolios using a few stocks that are given as inputs. I am having some trouble trying to find if these results are correct. My biggest hesitation is that ...
1
vote
0answers
24 views

Where to Find Foreign Countries Index Option Data

OptionMetrics database contains option data for several US indexes (SP500, SP100...). But I don't see any option data for foreign indexes. Is there a place from which I could get/purchase the options ...
1
vote
0answers
22 views

Commodity Selection Index Derivation

The formula for the CSI, as found on page 111 of J. Welles Wilder's New Concepts in Technical Trading Systems (link), is as follows: I'm curious about the derivation. Multiplying the ADXR and ATR14 ...
1
vote
1answer
64 views

Bermudan Swaption

Is there an equation of the kind of call-put parity for Bermudean swaptions ? (maybe an inequality ) Is there an intuitive description of what would be an optimal exercise moment ? Intuitively I ...
0
votes
0answers
25 views

Cross-Sectional Multi-Index Model

I'm unsure how to find the covariance matrix in part (b) and what the residual deviations are. Any tips on how to tackle this?
3
votes
2answers
125 views

Verifying two properties of the Clayton Copula

So I'm trying to verify the first two properties of a copula for the Clayton model. The first two properties being: $C(u_1,…,u_d)$ is non-decreasing in each component, $u_i$ The $i^{th}$ marginal ...
1
vote
0answers
16 views

Show that the variance of the portfolio market portfolio is function of the betas of its consituents [closed]

Let us assume that the market portfolio consists of n assets. Given that the return of the market portfolio can be written as $r_m = \sum_{j=1}^{n} w_jr_j$, we have that $\sigma^2_m = E(\sum_{j=1}^{n} ...
2
votes
0answers
39 views

Ito Diffusion with Change of Measure

Let $(X_t)$ be an Ito diffusion with speed $(V_t)$, under a probability measure P. Could there exist a change of measure to a probability measure Q, with Q ~ P, under which $(X_t)$ is an Ito diffusion ...
-2
votes
0answers
55 views

Show that the variance of the market portfolio is the weighted average of the covariance of its constituents with the market portfolio itself [closed]

Let us assume that the market portfolio consists of n assets. Given that the return of the market portfolio can be written as $r_m = \sum_{j=1}^{n} w_jr_j$, we have that $\sigma^2_m = E(\sum_{j=1}^{n} ...
2
votes
1answer
41 views

SMB data for 3-factor and 5-factor are different on French's website

Does anyone know why the SMB data published in the 3-factor and 5-factor data files on French's website are different? Which one should be used then?
1
vote
2answers
30 views

How to obtain annualized IR from t-monthly IC?

When we checking the relation between some factors and Stock price, we could use Information Coefficient(IC) to meausre. And then I already have t-monthly IC for each factor, and I need to calculate ...
1
vote
0answers
45 views

Geometric Brownian Motion with Dividends

I am working on a problem and had a quick question. I understand that for Geometric Brownian Motion we use the formula: $$X_{t_n} = X_{t_{n-1}} + \mu X_{t_{n-1}} \Delta t + \sigma X_{t_{n-1}} \...
1
vote
1answer
41 views

Does it make sense to combine different modified durations?

Does it make sense to aggregate different modified durations into one overall duration measure? In the context of insurance liabilities: ...
2
votes
0answers
45 views

Risk-Neutral Pricing with Regime Switching

As the title suggests, I am currently trying to implement a dual regime-switching options pricing model. In its simplest form, I am fitting a risk-neutral GARCH(1,1) to a crash and normal regime. ...
2
votes
0answers
48 views

When to stop training?

I have built a deep reinforcement learning based portfolio optimisation agent. At a high level it is using macro economic data, valuations of the assets and a few technical indicators as the features. ...
1
vote
0answers
17 views

How to calculate/estimate CLV for our odd subscription-based business model [closed]

I'm working on a school project where I and other group members come up with a business idea and write a paper containing all necessary information about the business, like the business model, revenue ...

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