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11 views

Random Forests - Relationships

This question relates to the use of random forests in finance and the relationship between the number of features, the observations, and the number of trees. Consider the relation between an RF, the ...
0
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1answer
16 views

Subadditivity of cvar(R)، R is random vector

$R=(R_1,\ldots,R_n)$ is random vector in $L^1(\mathcal{R}^n)$. Then is it true that $$ \operatorname{Cvar}(R_1+ \cdots + R_n) \le \operatorname{Cvar}(R_1) + \cdots +\operatorname{Cvar}(R_n)? $$ Can ...
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1answer
24 views

stock specific volatility

I was unsure about the precise definition of "stock specific volatility". Used in this question "A stock has beta of 2.0 and stock specific daily volatility of 0.02. Suppose that yesterday's closing ...
0
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1answer
32 views

Really simple question regarding options. (Amateur level)

I'm just starting to educate myself on trading and financial instruments and I have what to me seems like a somewhat stupid question but I'd like to pose it nontheless. If I have an option to sell ...
0
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2answers
43 views

Market maker's Operating Model

I got a question about the liquidity provider's operating model. Really hope if someone can take a look and share some thoughts! Scenario: Say an ETF investor wants to offload a million ETF shares; ...
2
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0answers
48 views

Model-Free Option Pricing

From Breeden and Litzenberger (1978) and subsequent work, we may find the risk-neutral density $q_{S_T}$ of $S_T$ from European option prices - assuming there are enough traded options (e.g. SPX) via ...
-2
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0answers
28 views

Performance attribution of a fund manager

I am given the following data: 1) the monthly sector (consumer staples, utilities, tech, etc.) exposures such that they sum to 100%, but not their individual returns. 2) the fund's monthly returns. ...
1
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1answer
45 views

FX Futures pricing formula

I'm reading Paul Wilmott's Introduces Quantitative Finance and stuck a bit with formula $F = S(t)e^{(r-r_f)(T-t)}$ for FX futures pricing. I don't get how to incorporate $r_f$ into the formula, could ...
0
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0answers
13 views

Arbitrage price and American option

I'm studying American Options. If I have $X=(X_n)$ an American option, it is not possible to determine a self-financing predictable strategy ($\alpha, \beta$) that replicates the option in sense that $...
0
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0answers
9 views

Bootstrapping with QuantLib using deposit rates and Swap rates

I'm trying to bootstrap and to get a zero coupon yield curve with maturities ranging from 2019 to 2059 Here is my code: ` ...
2
votes
1answer
22 views

Valuation of Cash-Or-Nothing option

Studying options pricing, I'm stuck with the following problem: The price of a stock is described by the dynamic: $$dS_t = \mu\, dt + \sigma\,dW_t$$ Compute the fair price of a Cash or Nothing ...
0
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0answers
16 views

is there a specific design pattern in C# to model a yield curve into the NS model?

I successfully managed to have a nice NS model to a yield curve I am studying using R, while I am still beginner in C# I wonder if there is a specific design pattern I should follow in order to put ...
1
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0answers
29 views

Portofolio optimization using ARMA-GARCH-EVT-Copula

I am currently trying to do some portfolio optimization by reproducing the methodology found in Sahamkhadam, Stephan & Östermark (2018) ("Portfolio optimization based on GARCH-EVT-Copula ...
1
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0answers
22 views

Generalisation of calendar arbitrage condition to options on futures

This question has discussed the condition on which calendar arbitrage opportunities arise for European call options on a stock. Do similar criteria exist for European options on futures? The most ...
0
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0answers
15 views

Spread vol for interest rate spread options in normal environment

Suppose I am long spread option with underlying : rate A - rate B. The vega on the option would be positive. But if I want to compute the option vega with respect to individual rates, can I use the ...
0
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2answers
59 views

Advantage of continuous time stochastic calculus over discrete version?

I'm new to the stochastic calculus, and I keep converting the continuous stochastic differential equation to its counterpart in discrete time, such as the autoregressive models. I wonder in practice, ...
2
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1answer
39 views

Is the Non-discounted Bachelier call option price a Martingale?

My math finance professor once said someting that I can't make sense of. Hope you can answer: For a foward process the non-discounted price for a European call option under Bachelier is $$C_t = \...
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2answers
58 views

Is there any funds that do market making?

In spite of banks, market making firms, brokers is there any funds that specially do market making?
0
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1answer
43 views

Cash Flow Hedge Accounting

In the context of hedging a fixed rate foreign currency liability with a receive-fixed pay-fixed CCS is known that in order to assess the effectiveness of a cash flow hedge the ratio of the change in ...
0
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0answers
21 views

Milan Stock Exchange model [on hold]

I would like to ask whether some of you know what kind of model (order driven/quote driven/hybrid) is used within the MAT market at Milan Stock Exchange or alternatively where is this information to ...
0
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0answers
31 views

Portfolio Return Decomposition

Barra gives factor weights for a common set of factors, for each asset. Given a long-short portfolio, is there a way I can combine the individual factor weights to get the factor exposures for the ...
0
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0answers
20 views

Why does an American option on a continuous dividend paying stock have a critical price above which it is optimal to exercise early?

An American call on a continuous dividend paying stock must be above its intrinsic value, i.e $c(t)\geq\max(S_t-K,0)$. Why is there a critical price above which it is optimal to exercise (i.e. we ...
1
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0answers
22 views

$\beta = 1$: Simulation of SABR and whether a solution is *exact*

Quick question regarding the conditional distributions (SABR is just an example here) Consider $$dS_t = \sigma_tS_tdW_t$$ $$d\sigma_t = \alpha\sigma_tdV $$ $$dW_tdV_t=\rho dt$$ Hence a SABR process ...
0
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1answer
39 views

Chorent risk measure with superaddative

In some definition of chorent risk measure Superadditive is one of the properties I don't understand Why? With subadditivity and homogeneous CvaR is convex, but if we assume another definition for ...
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0answers
17 views

What kind of standard deviation? [on hold]

Can someone help me convert the following standard deviation into something I can actually use e.g. in Excel? Also I don't understand why the T-1 is taken to the power of 0.5? The problem at the ...
0
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2answers
36 views

Will the Delta of an Option always be the same irrespective of the underlying stock price?

Suppose, under the Black Scholes model we keep all the parameters the same except that we vary the asset price. Will the Delta of the option always remain the same?
2
votes
1answer
71 views

Why did high yield corporate bond ETFs tank during the great recession

My apologies if this is not mathematical enough for this outlet. My understanding of the pricing of a bond ETF is that lowering interest rates drive the price up and increased risk of default drives ...
2
votes
0answers
31 views

Is $\sigma_{1} = \frac{\sigma_{\tau}}{\sqrt{\tau}}$ suitable for volatility scaling?

It seems to be the de-facto method; and I see how we get it from log-normal assumption. However volatility scaling seems to be way more sensitive to $\tau$ than mean scaling -- as in two ~ 2 times (...
2
votes
1answer
54 views

Trading Vol with options

One can trade vol swap to get exposure of the volatility of the underlying security in a 'clean' way. On the other hand, we know that vol swap, theoretically can be replicated by a dynamic position of ...
0
votes
1answer
45 views

Duration. Floating rate note

I don't understand why the duration of a floating rate note equal to the time to the next coupon payment? Please, look at my calculations. Here: P - is price at moment 0.
0
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0answers
12 views

Investigating the relationship between mutual fund alphas and market volatility

I am writing a master thesis on the relationship between mutual fund alphas and market volatility. As I have never performed an empirical analysis before, I would like to have some opinions on the ...
1
vote
1answer
51 views

Pricing with local volatility for derivatives beside options

Say I have calibrated an local volatility mode to market data on a forward on stock X. Say I want to price a derivative Y that is NOT a call/put option. What is the (or one of many) general strategy ...
0
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0answers
23 views

Framework for hedging fx and utilizing correlation between asset returns

Can anyone point me in a direction (research paper, books, ..) which developes a framework/strategy for hedging currency exposure for an international bond portfolio? This paper finds optimal ...
6
votes
1answer
47 views

Control variate for pricing a best of assets option : $\mathop{{}\mathbb{E}}[ \max ( F^1_T,F^2_T, …,F^N_T )]$

I want to use Monte Carlo to price a best of assets derivative : $$\mathop{{}\mathbb{E}}[ \max ( F^1_T,F^2_T, ...,F^N_T )]$$ where the $F^i_T$ is the forward of the ith asset observed at expiry ...
0
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0answers
33 views

Doubt about metrics in the Performance analytics package of R [on hold]

I have a large database of daily returns on investment funds. I would like to know if to apply the performance evaluation metrics, such as Sharpe ratio, Information Ratio, etc., of the "Performance ...
0
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0answers
23 views

Monte Carlo Simulation with varying expected returns and volatilities

I have yearly CMAs which denote the 5-year forward looking returns and vols. These CMAs are updated every year. For example in 2004, the outlook for next 5 years is 11%, in 2005 the outlook is 10.8%. ...
0
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0answers
22 views

FX Options Greeks: Is there a meaning in converting the sensitivities values in different currencies?

Suppose you have a Call on JPY, domestic currency is USD The price will be in USD Let's say delta = 0.93 Does it make sense for any reporting reasons to convert this value into JPY ? What is even the ...
9
votes
1answer
88 views

Intuition behind Implied Volatility Surface

When looking at an implied volatility surface, are there some intuitive conclusions that one can draw from the shape? E.g. the steepness of the wings, the skew etc? If one for example compares two ...
1
vote
1answer
44 views

Reading List (Advanced Alpha Design)

I am busy working on a getting started guide for advanced quantitative finance (for alpha design) and have been searching for the seminal books/literature for the field. So far I have the following ...
3
votes
0answers
52 views

Pricing eurodollar futures

How are Eurodollar futures priced in practice? What I already know: The implied 3 Months rate by the futures is 100-price, since it matches the payoff. Using daily LIBOR rates, one should be able to ...
2
votes
1answer
88 views

Overlapping vs Non-overlapping returns

Suppose I want to estimate the following regression: $R_t=\alpha + \beta X_{t-1} +\epsilon_t$. Where I use asset returns as the dependent variable. Both overlapping as well as non-overlapping returns ...
0
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0answers
30 views

OIS vs Libor for cross currency

I would like to understand the convention for discount rates fro cross currency swaps. It seems to be market convention (Australia) to discount collateralize positions with OIS and uncollateralized ...
1
vote
0answers
24 views

Swaption pricing and strategies

I am looking for resources (books, papers, websites, etc.) that deal with Vanilla and Exotic swaptions from a more advanced and quantitative perspective. I am interested in both the pricing side (e.g. ...
0
votes
1answer
30 views

Where can I find the formulas to compute the Greeks for European Call and Put Options Assuming no annual dividend yield?

Every formula I come across involves a $q$ (the annual dividend yield). Where Can I find the formulas to compute the greeks assuming no dividends?
1
vote
1answer
37 views

Equivalence of formulas for pricing the Delta of a European Call Option?

I came across two formulas to compute the Delta of European Call Options. The First: $\frac{\partial C}{\partial S} = e^{(b - r)T} N(d_{1})$ The Second: $\frac{\partial C}{\partial S} = e^{-qr}N(d_{...
0
votes
1answer
45 views

Black Scholes Replication If Underlying Does Not Move?

Let's say you are long a call and want to replicate that call buy being short underlying and long bonds. If the underlying moves up in the next period but not enough to cover theta, the option ...
2
votes
0answers
58 views

Ito's lemma for special case

Assume HJM framework and define the yield for a fixed maturity $$ Y_\tau(t) := Y(t, t+\tau) = -\frac{\ln(P(t, t+\tau)}{\tau} $$ I would like to write the SDE of this process. This reduces to the ...
-2
votes
0answers
18 views

How can i insert a if condition in my loop to create returns for my formation period [on hold]

I'm trying to implement a momentum strategy. To do this i need to sort my stocks based on their return in the previous 11 mths. My current code works quite well: ...
0
votes
0answers
18 views

predefined model structure for stock data

I've signed up for stock data service (IEX Cloud). I now want to fetch and save the data locally. I will need to design the ERD, is there a pre-defined open-source model (preferably Django) that I ...
1
vote
1answer
21 views

Where do the zero returns in QMNIX (AQR Market Neutral) come from?

QMNIX, Which is a market neutral offering from AQR, has a surprising number of totally flat days. https://finance.yahoo.com/quote/QMNIX%3FP%3DQMNIX/history/ Looking at the returns, 124 of them, which ...

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