All Questions

6
votes
1answer
90 views

Principal Components Analysis on overlapping contracts

I am conducting several PCAs on the gas forward curves (months, quarters, seasons, calendars) for hedging purposes which give me some rather reasonable and stable results. However, these contracts ...
3
votes
0answers
43 views

Martingale positive price process

I hope you can help me with this problem. In my lecture notes, my professor stated that for a state price deflator $\phi\in L_{n+1}^2(P, F)$ (F being a filtration) and a strictly positive price ...
1
vote
0answers
38 views

Does it make sense to subtract VaR from spot shocks?

I have a model to compute the Event Risk (in dollars) from a shock to the spot price of an asset. I also have the 10-day VaR PnL for the same assets returns. These two numbers are then aggregated to ...
0
votes
0answers
72 views

Curve Building + Swap Pricing [duplicate]

Assume Swap means a USD Swap with standard conventions (semi-annual fixed payments and quarterly floating payments, etc).
10
votes
1answer
290 views

Variance swap volatility - ATMF vol, Skew and Curvature

In a pure diffusion setting, it is a well known result that the volatility $\sigma_T$ of a fresh-start variance swap of maturity $T$ as seen of $t=0$ verifies \begin{align} \sigma_T^2 &= \Bbb{E}_0^...
1
vote
0answers
37 views

What should the half-life be in EWMA when calculating VaR from EWMA?

If we want to calculate an $x$-day VaR ($x$ is some time period in days) from an Exponentially Weighted Moving Average (EWMA) of vector of returns, what should the half-life in the decay factor in ...
1
vote
0answers
31 views

What are the different indicators to measure historical volatility for stocks on individual basis?

Google search shows there are three indicators to measure volatility: 1. Average True Range 2. Standard Deviation / Variance 3. Bollinger Bands. What are the indicator(s) that you use to identify ...
3
votes
1answer
99 views

Do *all* non-dividend paying assets have the risk-free instantaneous return rate under the risk-neutral measure?

For simplicity let's consider a 1D BS world. The only source of randomness comes from the Brownian motion dynamics $dB_t$. The risk-free rate is $r$ (one may assume it as constant for the time being). ...
4
votes
1answer
103 views

Expected payoff at future time

Let $a$, $b$, $c$, and $e$ be constants, $W_1$ and $W_2$ be Brownian motions with correlation $\rho$, and $f(t)$ and $g(t)$ be deterministic functions of time. Let $X$ satisfy $$d(X(t))=(aX(t)+ef(t)g(...
0
votes
1answer
69 views

Transform of payoff function $w_c=(\sqrt{y}-K)^+$ [closed]

I am working on a project where I price EU call options written on the VIX index. The payoff function of interest looks like $w_c=(\sqrt{y}-K)^+$ where K is the strike price and y is the value of $...
1
vote
0answers
50 views

Creating a hedge portfolio out of 10 assets

Suppose I have historical return data on 10 assets. How can I create a hedge portfolio that prices all these assets in a factor model? I have chosen 3 factors: excess market return, SMB and HML from ...
3
votes
1answer
87 views

Value-at-Risk for a portfolio model with Gearing

My models: Say I want to construct a portfolio so I maximize my expected return while keeping my risk (measured by Value-at-Risk) lower than my risk target. $$\max \sum x_i \mu_i \\ VaR_{0.05} \leq \...
1
vote
0answers
39 views

Valueing a Short future contract with dividens [closed]

A forward of an underlying paying a yield $q$ can be priced with the equation: Price $= S_0 e^{(r-q)*t}$ or Price $= (S_0-I)e^{rt}$ Where $S_0$ = Spot price, r = interest, q = dividend yield, I = ...
0
votes
1answer
47 views

Black Scholes modified boundary conditions

Compute the price of the payoff $(2\log(S(T))-K)^+$. Before I do any algebra, I want to make sure I understand. To solve this problem, I need to solve the Black Scholes PDE with boundary condition $C(...
2
votes
3answers
146 views

Hedging a CDS sold

How would a bank that sold a CDS to a client hedge its position? Is there a replication method similar to what is done with option hedging or other methods used? Many thanks
0
votes
0answers
15 views

Binomial correlation measure in the trivariate case

I have a question about the binomial correlation measure at page 530 in Hull(2009), Options futures and other derivatives (7th Edition) which is defined for the bivariate case as: $\beta_{AB}(T)=\...
1
vote
1answer
88 views

A positive Sharpe ratio when portfolio loses money, can that happen or bug in my code?

I'm having a trouble calculating (annualized from daily performance) Sharpe ratio, even though I've read some related posts here. Say I have a daily performance, for example: $$[1.15, 1.2, 0.7]$$ ...
-2
votes
0answers
26 views

monthly conditional volatility using EGARCH model

I need the conditional volatility values using the egarch model in eviews. The result of the estimation that I get is a table where there are coefficients, p values....My question is that how could I ...
1
vote
1answer
49 views

Predicting microstructure momentum in market making

If I have a market maker which is compelled to provide quotes on both sides of the market, I am exposed to risk of quadratic losses (vs my linear gains during normal operations) during times when the ...
0
votes
0answers
34 views

Another variation of the 'Sharpe ratio' in CVaR-based portfolio optimization?

Question What is the ratio S(p) shown below? Do we have a name for it like 'Sharpe ratio'? The ratio above is introduced in the academic paper Optimal portfolio selection in a Value-at-Risk framework ...
0
votes
0answers
70 views

Calculating min/max price range using volatility

I'm trying to reconcile two methods of forecasting price ranges with say 95% confidence over a 50 day period given the annual365 IV say 19.1% = 1% daily volatility take the daily standard deviation ...
2
votes
0answers
17 views

Convolution of generalized hyperbolic distribution

I have a question concerning the convolution of generalized hyperbolic distributions. Proposition 6.13 of McNeil, Embrechts, Frey states the following: If $X$ has a $d$-dimensional generalized ...
3
votes
1answer
64 views

The conditional mean of a product of standard Brownian motions

Suppose $\{W_t, t>=0\}$ is a Standard Brownian Motion. How to compute $ \mathbb{E} \left[ W_2 W_3 \vert W_1 =0 \right]$? We know $ W_2 \vert W_1 = 0 \sim N(0,1)$ and $ W_3 \vert W_1 = 0 \sim N(0,...
1
vote
0answers
40 views

QuantLibXL no intraday pricing, even with QL_HIGH_RESOLUTION_DATE enabled while compiling

I built QuantLibXL myself following the instruction here: https://www.quantlib.org/quantlibaddin/build_qlxl.html And in the QuantLib code, I turned on the QL_HIGH_RESOLUTION_DATE flag, before I run ...
2
votes
1answer
45 views

Markowitz portfolio optimization and CAL [closed]

Just had some questions regarding the efficient frontier and the CAL. As i understand it the point where the CAL is tangent to the efficient frontier is the optimal mix of risky assets. However I also ...
1
vote
1answer
62 views

Risk-neutral density from spot prices?

I am currently working on a university project and I hope someone can help me out with a rather silly question :-) I want to analyse the change in the shape of risk-neutral density functions of spot ...
3
votes
0answers
58 views

Is there a more efficient data structure to implement binomial trees than 2d array?

I'm just curious what is the "industry standard" for implementing a binomial tree (if "standards" exist in this case). For simplicity, let's just talk about the simplest trees with recombining nodes. ...
1
vote
0answers
30 views

Reason for stale sovereign CDS spreads (e.g. Greece)

I have a dataset of CDS spreads for European sovereign from Thomson Reuters Datastream. I noticed for some entities in some timeframes, spreads are essentially stale. For example in the case of greece ...
4
votes
0answers
74 views

Zero-rebate barrier option pricing under the Heston model

I'm trying to derive an approximation for the zero-rebate barrier option under the Heston model: $$dS_t=\mu S_tdt+\sqrt{v_t}S_tdW^S_t$$ $$dv_t=\kappa(\bar{v}-v_t)dt+\eta\sqrt{v_t}dW^v_t,\quad d\langle ...
1
vote
1answer
102 views

Is studying R quantstrat worth the effort for an individual trader? [closed]

I see at least two problems. The R package quantstrat is poorly documented. And one must have dividends adjusted data. Otherwise the test results will be irrelevant.
1
vote
0answers
22 views

How to measure effectiveness of CDS hedging

In a fixed income emerging markets portfolio investing in Sovereign and Corporates, CDS on governement bonds are used for hedging credit risk. To be clear CDS are used to hedge both the exposure of ...
4
votes
0answers
65 views

Whats the big deal between volatility and the risk free rate?

I am trying to understand asset price volatility. Many of the news articles I read link how stock market volatility is linked to asset price volatility? To give an example, in Mike Mackenzie's (...
6
votes
0answers
52 views

Formal proof market incompleteness under jump diffusion

Does anyone have formal proof of markets incompleteness under jump diffusion ? I am familiar with the intuitive approach as mentioned in Tankov (delta), yet I am looking for a formal approach and ...
1
vote
1answer
45 views

European put price when stock price is 0 before maturity

According this answer, https://quant.stackexchange.com/a/39298/29108, the European put price (with maturity $T$) at time $t$ for a stock whose current price is $0$ should be the strike $K$ discounted ...
3
votes
1answer
102 views

Trading Jargon - Interest Rate Swaps / Bond Trading

I was going through some reports but having hard time with the jargon. When I google them online I came across the page: http://volcurve.blogspot.com/2007/10/carry-and-roll-down-back-to-basics.html ...
2
votes
1answer
46 views

QuantLib CDS pricing error: negative time given

I am new to QuantLib, and I am using it to price CDS. Following is my python code: ...
2
votes
1answer
44 views

How to determine the risk-neutral measure in a Heston model?

To clarify, I'm quite familiar with the risk-neutral pricing framework, and I know one can efficiently Monte-Carlo a Heston model via the non-central $\chi^2$ distribution approach. But so far we're ...
2
votes
2answers
62 views

Is the sharpe ratio calculated taking the standard deviation of the portfolio or of the excess return?

Does the formula consider the standard deviation of the excess return: $$\frac{𝑟−𝑟_𝑓}{𝜎{(𝑟−𝑟_𝑓)}}$$ or that of the return: $$\frac{𝑟−𝑟_𝑓}{𝜎{(𝑟)}}$$
2
votes
0answers
39 views

Trades vs Cancel orders

In case of designing high frequency algorithms, do people treat all changes in the mid price similarly. What I mean is, if there is a change in the mid price due to a trade or there is a change in ...
0
votes
0answers
75 views

Interview question on interest rate spread trade

Consider this interview question: Tell me how you'd construct a risk neutral cross country trade on the 2 year – 10 year interest rate spread in Germany and the U.S. What does "risk neutral" mean ...
3
votes
0answers
64 views

Alternative Method for Determining Option-Implied pdf

As I am refining a pricing model to incorporate skew, and not just ATM volatilities, I need to create random realizations of the underlying consistent with the skew-implied pdf. When searching, one ...
2
votes
0answers
92 views

The “Universal Model” by Justin Sirignano and Rama Cont

In the nicely written article https://arxiv.org/abs/1803.06917 by Justin Sirignano and Rama Cont, they explained that their model is universal and stationary. I am a bit confused about some questions. ...
2
votes
0answers
64 views

How do you numerically solve the Dupire Local Volatility PDE in log moneyness-time space?

I am trying to implement a numerical solution to price vanilla calls. I am using the Dupire equation in log moneyness-time (k = ln(F/T)) space as per below PDE I have tried solving it using a fully ...
2
votes
2answers
74 views

Failing Jarque-Bera test but residuals looks normal on q-q plot and histogram

If I'm failing the Jarque-Bera test but the residuals still appear to be normally on a qq plot and histogram, is it acceptable to say that my residuals are approximately normally distributed? Asked ...
1
vote
1answer
56 views

How to modify binomial tree to incorporate one more asset?

I wonder, what would happen if we use the binomial tree to price exchange option, an option to exchange one asset for another at the expiry date. Payoff is $\max(S_1-S_2,0)$ For instance, I have two ...
1
vote
1answer
52 views

Portfolio Delta - long call, long put and short call

First and foremost, I'm trying to understand why you would construct a portfolio made up of long calls, long puts and short calls. I find this really abstract and confusing. I've tried drawing the pay-...
1
vote
0answers
54 views

Methods for calculating Expected shortfall

Let B1, B2 be two defaultable zero-coupon bonds maturing in 1 year, each with a face value of $100. Assume: each bond is priced at 90 dollars each bond has a 4% probability to default within 1 year ...
0
votes
1answer
47 views

Co-variance of portfolio A with Portfolio B

I'm really just doing this out of curiosity so my apologies if this is a noob question but, I'm trying to calculate the correlation between two separate portfolios. I've used the following formula ...
1
vote
0answers
38 views

Decomposition of interest rate risk [closed]

Hi I needed some clarification on something. I have three variables: V1 which is an indicator of an interest rate risk premia V2 which is an indicator of a credit risk premia V3 which is an ...
1
vote
0answers
32 views

CDX funded vs unfunded returns timeseries

I've been asked to provide a CDX.NA.IG unfunded total returns timeseries, for which I've been able to use a Bloomberg ticker LX01TUUU Index. This works fine - it's called an unfunded total returns ...

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