All Questions

0
votes
0answers
5 views

Finding Equity Of A Home Bought Using A Mortgage

Let's say I buy a house using a mortgage where the following information is true: The house's original price was $100,000. A down payment of 20% was required. I get a mortgage with a 4.5% interest ...
0
votes
0answers
9 views

Why no median-CVaR optimization for portfolios?

Question Since CVaR is a concept that can be applied to all probability distribution, even if they do not follow normal distribution, I thought CVaR should be more concerned with median, not the ...
7
votes
1answer
370 views

Risk-Neutral CAPM

In the paper Measuring Equity Risk with Option-implied Correlations, Buss and Vilkov replace the standard CAPM beta: $$ \beta_{iM,t}^P=\frac{\sigma_{i,t}^P\sum_{j=1}^N w_j \sigma_{j,t}^P\rho_{ij,t}^P}...
0
votes
1answer
46 views

Black-Scholes volatility implied by stock prices only

I was solving Problem 2.47 from T.F. Crack's "Heard on the Street". I think that the answer given in the book is not correct and I would be thankful if you tell me, where I am mistaken. Question 2....
1
vote
0answers
22 views

Constructing Portfolio Beta

Suppose I have a portfolio with securities with different history. Say some securities have 15-20 years of history and some are like Uber or Lyft, which has limited history. There are assets with 1/2/...
1
vote
0answers
6 views

How to add Risks-Not-In-VaR (RNIV) to VaR under Basel III

I am trying to generate/prove the magnitude of the over-conservativeness of the regulatory VaR (internal models) under Basel III against what a more accurate VaR would be. However, I can't seem to ...
2
votes
1answer
249 views

Best way to buy and sell large volumes of crypto

I had a few questions about how to properly execute a large order of crypto currency without moving the price much. I know a lot of funds employ a TWAP/VWAP algorithm to liquidate or purchase a large ...
0
votes
2answers
33 views

Why can we assume that asset return rates are normally (or lognormally) distributed?

In many theories of financial mathematics it is assumed that asset return rates are normally distributed (e.g. VaR models) or lognormally distributed (e.g. Black-Scholes model). In practice, asset ...
0
votes
0answers
54 views

Portfolio - Default Probability

Suppose we want to identify the frequency of default on a portfolio with a 1000 loans. In the independence case, each firm’s default process follows a Bernoulli distribution with parameter $p = 0.01$. ...
1
vote
0answers
29 views

Are the returns in this regression signed returns?

In this paper about combining multiple alphas are the returns signed returns? if not wouldn't they be mean zero? Also, it mentions "realized alpha returns" - does that just mean "realized" past alpha ...
1
vote
1answer
30 views

Covered Interest Rate Parity with FX Spot-Adjustment

The Covered Interest Rate Parity for FX is often quoted simplistically as $$ X_T \quad=\quad X_S \cdot \frac{D^{base}_T}{D^{quote}_T} $$ where $X_t$ is the (projected) FX rate at time $t$ (denoted as $...
0
votes
2answers
31 views

Is it possible to adapt Fama French Model with a 6 factor Model?

I am currently working on my thesis and I was wondering if it was possible to add a new factor to the five model one. This new factor would include the ESG's characteristic of the stock. I would like ...
2
votes
1answer
133 views

Pricing under risk-neutral probabilities for weird derivatives?

I would really appreciate some help to value a weird derivative that I've found in an assignment: $$ X=(S_{T_1}-k)^{+} = \max(S_{T_{1}}-k;0) $$ which expires at time $T_{2}$ and uses the price at ...
7
votes
4answers
14k views

How to construct a Risk-Parity portfolio?

If I would like to construct a fully invested long-only portfolio with two asset classes (Bonds $B$ and Stocks $S$) based on the concept of risk-parity. The weights $W$ of my portfolio would then be ...
0
votes
0answers
18 views

Distribution of the Information Ratio // Mean and Variance Product

We are investigating the distribtuion of the information ratio. However, instead of using the original information ratio defined as \begin{equation} IR=\frac{E(r_1)-E(r_2)}{\sqrt{Var(r_1-r_2)}}, \end{...
1
vote
1answer
39 views

Forecasting a seasonal series with R

I am working with the program "R". I used the command "seas (X-13)" to deseasonalize my quarterly series, then I did the forecast with it. Therefore my forecast is in deseasonalized terms. Now, I was ...
1
vote
1answer
91 views

Monte Carlo simulations in Python using quasi random standard normal numbers using sobol sequences gives erroneous values

I am trying to perform Monte Carlo Simulations using quasi random standard normal numbers. I understand that we can use sobol sequences to generate uniform numbers, and then use probability integral ...
0
votes
1answer
45 views

When a bank enters a swap with a counterparty, when does it decide to use a OIS curve as its CSA Term, versus a counterparty specific “CSA Curve”?

What determines whether a swap should be discounted against a standard OIS curve VS a 'custom' CSA curve specific to the swap's counterparty? (such custom curves are marked as spreads to some base ...
1
vote
1answer
182 views

Crossing the spread as a ML signal

In the optic of high-frequency trading, most of the standard trading algorithms work on the principle of mid-price prediction or mid-price movement prediction. However a big drawback of this technique ...
0
votes
1answer
41 views

Tracking historical short interest

I am looking for a source of historical (more than one year) short interest in a specific equity. NASDAQ provides only one year of short interest history. I am interested in looking back 2 to 3 years. ...
2
votes
1answer
2k views

How to compute for basis adjusted forward rate?

To give you a brief background, I'm valuing a fixed-for-float Interest Rate Swap (IRS) using Bloomberg. I put in a notional amount in (USD) and a assigned 6MO USD LIBOR as the reference index for the ...
4
votes
3answers
143 views
+100

PCA: How to select a smaller set of the original features that best represent first PC with minimal contribution to the other PCs

I have performed PCA on a covariance matrix. I have 24 original features and subject to some constraints over which features are used i would like to chose the combination of features that best ...
1
vote
1answer
45 views

Calculating PD of commercial bank loan

I have two main options to calculate PD of a loan in a commercial bank; with and without machine learning. On one hand, there are traditional methods such as Merton or KVM. On the other hand, I could ...
1
vote
1answer
66 views

In-sample volatility measurement

I would like to know what is the most reasonable way to measure volatility in a sample of past observations. Aside from standard deviation, are more complex models like GARCH used for (historical) ...
0
votes
0answers
12 views

Longstaff Schwartz with future conditional coupons

I've implemented the L-S algorithm for a simple put option. I want to value a more complex derivative which has future conditional coupons which only occur if the option is in the money. How would I ...
7
votes
1answer
585 views

Up and Down days in GBPUSD and a Filter

I want to study if the odds of an up or down day in a forex pairs is 50-50. I just count the total number of up and down days in X years and compare it with the total days. The results are very ...
0
votes
2answers
527 views

Is there any public data to get OIS for differal time (1d, 1W, 1M, …, 10Y)?

I want to get data of Overnight Index Swap, also known as OIS rate, there is any public why to get this always from yesterday? For example, I want to get EFFR(Effective Federal Funds Rate), I can get ...
1
vote
0answers
23 views

Understanding the ZABR model (an extension of SABR)

http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf In this acticle the SABR model is first presented in another form ( see equation 7 in the article ) and then extended to the so called ZABR ...
0
votes
2answers
75 views

Transaction costs in option market

The transaction costs in option market could be quite large. The bid ask spread of a SP500 firm could be around 15% of the mid-quote when I check the data. Since I do not have data on transaction ...
0
votes
0answers
39 views

A stringent test of stock return predictability? The role of one-sided hypothesis tests

A stringent test of stock return predictability? The role of one-sided hypothesis tests... In a well-published paper, Trading Volume and Cross-Autocorrelations in Stock Returns TARUN CHORDIA ...
1
vote
0answers
46 views

Is it necessary for $P(K, t) - P(K + s, t) \geq se^{-rt}$ to hold?

Let $P(K, t)$ be a put option with strike price $K$ and expiration time $t$. Let $s > 0$. Is it necessarily true that the inequality $$P(K, t) - P(K + s, t) \geq se^{-rt}$$ holds? I know that ...
3
votes
1answer
125 views

Finding optimal trading of option on a foward

Assume you have a option on a forward $F$ with a payoff: $\max(F_T - K, 0)$. Assume also, that you have a bullish view on the forward in such a way that $E_{0}[F_T] > F_0 = E_{0}^{*}[F_T]$ (where ...
1
vote
0answers
26 views

Pricing call option on bond under CIR model by simulating noncentral chi square distribution

In the original paper of CIR model, there is a pricing formula about call option on bond $$ \begin{array}{l}{C(r, t, T ; s, K)} \\ {=P(r, t, s) \chi^{2}\left(2 r^{*}[\phi+\psi+B(T, s)] ; \frac{4 \...
1
vote
1answer
58 views

Leverage constraints

I am trying to complete my project on Mean-Variance Leverage Optimization, and I have found lots of helpful advice on this forum. I wanted to ask you if you have some idea on how to implement a ...
1
vote
0answers
43 views

How do you hedge with delta futures if payment is unsure?

A Czech company has a payable of 1,5 mil EUR that has got a settlement at the end of the current month and at the same time it is expecting a payment of 1,5 mil EUR at the half of the current month ...
1
vote
0answers
46 views

Mean-variance portfolio optimization: methods for superior estimates of returns

Leaving aside the aspects related to the estimation of the variance component (all the latest techniques to compute a stable covariance matrix of a given set of assets such as simple shrinkage, Ledoit-...
1
vote
0answers
47 views

Why don't we build the discounting curve and projection curve from bonds

We know that we always build the discounting curve and projection curve from money market instruments, index Futures, interest rate swap and OIS Libor swap (depends on the period). But why don't we ...
5
votes
4answers
722 views

Where can I get equivalent of 3 months libor or swap historical data?

Please note: I have already checked your standard "Historical data sources" link, but it does not have the data I need: I am looking for 5 years of libor/swap data for major currencies. Daily, or ...
2
votes
3answers
612 views

CVA DVA and Bilateral adjustment

I've already computed the CVA\DVA and now I would like to compute the bilateral adjustment. Does anyone know the relationship between the CVA\DVA with the bilateral adjustment? I mean a paper, ...
1
vote
0answers
24 views

How to apply multiplicative price seasonality to bond prices in quantlib?

Can someone please give a brief or any link which explains how to apply multiplicative price seasonality to inflation linked bonds in Quantlib using python modules. Have gone through most of the ...
3
votes
2answers
159 views

What is the economic reason for the equality in value of an American call and European call?

In a previous question this question came up. In my mind, if I'm holding an option at time t, then there are possible future price paths where at t+k the option will be ITM but at T the option will ...
1
vote
0answers
48 views

Does Vasicek interest rate model had any derivation that follows from a list of assumptions?

I can't find that anywhere online and It doesn't seems to me that this model originated come from intuition or some human motivation but rather it is coming from computerized curve fitting as all the ...
1
vote
1answer
58 views

Calendar roll terminology (buy vs sell)

I am trying to get the direction/terminology correct in futures calendar trading. Let's say I have two calendar futures contract where the prices are 100 and 102 reflecting the front and back ...
3
votes
0answers
41 views

Why not discount the dividend in the european put lower bound condition?

According to the european put lower bound condition: $ p \geq max(D + K \cdot e^{-r(t_2-t_0)} - S_0, 0)$ where $t_0$ is now and $t_2$ is maturity. Say $t_1$ is the dividend release time where $t_0&...
1
vote
1answer
30 views

Cross currency swap basis with USD added on the covered interest rate parity (CIP)

We know the adjusted covered interest rate parity (CIP): $$Forward = \dfrac{1+r\cdot\tau+b}{1+r^*\cdot\tau+b^*}Spot$$ Here $r/r^*$ is the risk-free foreign/domestic rate and $b/b^*$ is the cross ...
1
vote
1answer
107 views

Reducing pricing errors (Alpha) in the CAPM with Bitcoin

I have been trying to examine, using the CAPM, if Bitcoin belongs in the market portfolio or not. With 10 industry portfolios from http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library....
2
votes
1answer
70 views

Hedging with different volatility (Ahmad and Wilmott paper)

In their paper they show that: - if you hedge with the realised volatility, the present value of the total p&l is the difference between the option value based on the realised volatility and the ...
4
votes
1answer
78 views

Expected value of exponential of hitting time of GBM

We have a stopping time $$ \tau=\inf\{t\geq 0: S_0e^{\sigma B_t+(r-\sigma^2/2)t}=S^* \} $$ where $S_0,\sigma,r,S^*$ are constants and $S^*<S_0$, and $B_t$ is a brownian motion. I wish to compute ...
2
votes
1answer
387 views

Rblpapi millisecond resolution

I'm using Rblapi to get tick data, using the nice getTicks function. Much to my dismay the index is rounded to the second, while milliseconds time stamp could be provided. Tried returnsAs xts, fts(?) ...
1
vote
1answer
76 views

Discontinuous derivative payoff approximation

Consider a derivative of digital type which pays this kind of payoff at time $T$: \begin{align*} g(S_T,k) &= \begin{cases} P_0,~S_T>k \\ S_T, ~S_T\leq k \end{cases} \end{...

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