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4 views

Classic dynamic delta-gamma hedging in Python

I am trying to run a delta-gamma hedge for a Black-Scholes model in Python.The Euler disceretizatioin of the paths is the simplest possible. I wrote the code below but the PnL looks undesirable and ...
3
votes
1answer
32 views

Expense ratio in ETF price

I am examining the relationship between the price of an ETF and the index it is tracking (in this particular example, the Vanguard S&P 500 ETF (VOO) and the S&P 500 index). I can see the ...
3
votes
1answer
776 views

Currency risk USD>EUR>EGP

Seeking input on hedging risk on USD to Euro with a 3rd component of payroll issued in Egyptian Pounds. We are a US corp invoicing a Germany entity in Euro with massive payroll being paid in Egyptian ...
-2
votes
0answers
8 views

How to make profit from your own portfolio

Can someone please explain to me after creating my own optimized portfolio, how do I make profit from it? Do I make the portfolio and set it aside for a couple of years and then sell the stock in it? ...
1
vote
1answer
46 views

Backtesting model results, but backtesting output sampled at different frequency than model output

So, I'm trying to backtest a model that computes P&L. This model pulls sensitivities on a weekly basis and applies market shocks to these sensitivities to project quarterly P&L. I want to ...
1
vote
0answers
36 views

Banks' use of written interest rate options

I study US commercial banks data. I look at the notional amounts of their different OTC interest rate derivatives for the recent years. When I look at non-dealer banks (i.e. end-users), I find that ...
1
vote
0answers
16 views

Numerical Solutions to PDEs with Financial Applications

I am reading a paper by Richard White, Opengamma named Numerical Solutions to PDEs with Financial Applications. There is an implementation codes as stated in paper hosted at https://opengamma.com/...
2
votes
0answers
21 views

Change of measure for BGM (LMM) Model

I've been checking the demos for BGM (LFM) forward rate model. Here's a short reminder to help you follow: Now, take the following $$\frac{dL_j(t)}{L_j(t)} = \sigma_j. dW^j(t) = \mu_{ij} dt + \...
2
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0answers
10 views

tick/book data vs bar data, worth the infrastructure investment?

For reference, I am talking on behalf of a small group of math/stats graduate students as well as software engineers (we are 6 total), we know each other for years and decided to make a small (private)...
0
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0answers
26 views

Calculate the conditional variance-covariance matrix to optimal hedge ratio bekk

I estimated an MGARCH-BEKK model (using the R package BEKK). (BEKK= Baba, Engle, Kraft and Kroner; see Engle and Kroner (1995)) on time series of spot and futures prices. The estimated parameters are: ...
0
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0answers
21 views

Variance swap = delta hedged strip of options

Is there a paper that explicitly shows/demonstrates that a variance swap can be replicated by delta-hedging a strip of options? Thus far I have not found anything: papers mention it in passing ...
-1
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0answers
21 views

In US, is transaction cost of intraday trading less as compared to overnight trading?

In the Indian market, transaction charge for intraday trades is usually lesser than transaction charges of overnight trades. Charges in India Numerically it is approximately, 0.025% on the sell side ...
1
vote
1answer
271 views

Exercise Probabilities Vanilla Cap/Foor

When looking at the discounted pay-off formulas of a vanilla caplet and a vanilla floorlet $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_k-r_{cap},0)$ $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_{floor}-...
-4
votes
3answers
1k views

Value at Risk - Long/Short position

I have a simple question on the VaR for a portfolio that consists of a long and short position. Say I have a portfolio consisting of the following positions: long 1000 shares of stock X short 1000 ...
3
votes
1answer
42 views

Questions about beta, correlation, and covariance

Currently, I calculate beta, correlation, and covariance measures using daily log normal returns of Security A and Benchmark A. What would it mean if I were to use daily log normal excess returns in ...
0
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0answers
15 views

Normal default probability vs forward default probability/conditional default

is the diagram correct in calculating foward PD(conditional default) ? Or should the formula be Probability of default = probability of survival x forward PD Which of this is equal to marginal PD(...
2
votes
3answers
98 views

Pair trading - short / long the spread

I am wading into pair trading concepts. Here is one article I've read. I understand for these strategies our intention is to go long on one asset and short another, however I do not understand what ...
0
votes
2answers
115 views

Geometric Brownian Motion - Price Probabilities

I am modeling a stock price that follows Geometric Brownian Motion and have the following: $E(X)$ = .16 (16%) $\sigma$ = .24 (24%) $X_0$ = 95 $T$ = 1 (12 months) I am trying to find the ...
2
votes
1answer
82 views

Convert volatility to yield

I have an elementary bond volatility math question - if 5y black vol is 38 and normal vol is 68, and the yield is 1.85%, how do I calculate 1 stdev in yield terms? As in how many basis points (or ...
1
vote
0answers
17 views

How should I interpret the (insignificant) coefficients of Fama-French 3-factor model?

I am writing a mid-term thesis on the Fama-French factor model. I have built 5 portfolios sorted by the Book-to-Market ratio. The first portfolio is the lowest-BM group and the last portfolio is the ...
1
vote
1answer
45 views

Sensitivity Approximation - Crank Nicolson

I am looking into a new method of calculating sensitivities starting off with a proof of concept with Black Scholes PDE. Suppose I want to calculate Rho and take the derivative of the PDE (heresy!!) ...
0
votes
1answer
59 views

Black Sholes option pricing with all but Delta [on hold]

I'm trying to setup a little option pricing model in excel. I have all the information for the inputs (interest rate, IVs for different deltas, time to expiry, strike price, underlying price) but what ...
1
vote
1answer
59 views

What exactly does after tax “charge” mean?

My question isnt about the after tax part, but what is meant by "charge" as in "GE took a $6.2 billion after-tax charge". I get that GE would like to get rid of their LTC (Long Term Care Insurance) ...
1
vote
1answer
327 views

Volatility surface for Swaptions

I understand the volatility surface for swaption is built using implied vols of ATM swaptions. I had a question on the instruments that are used. Should the instruments used change depending on the ...
1
vote
0answers
27 views

Calculating the fundamental value of house price to separate bubble component from the price

The bubble in asset price is defined as the deviation of the asset value from its fundamentals, empirically Mendoza and Terrones (2008) measure the bubble as the deviation of an asset price from the ...
2
votes
0answers
50 views

Why do coefficients flip after the including a lag in the optimisation? implied volatility/skewness/ivspreads

I'm hoping some of you guys can help me out. I am applying the paramametric portfolio optimisation of Brandt, Michael W., Pedro Santa-Clara, and Rossen Valkanov. in which the weights on specific ...
3
votes
4answers
105 views

CAPM - Expected vs. actual returns

I'm trying to calculate alpha in excess of CAPM and have seen a few slightly different calculations for CAPM. The primary difference I am seeing is that some equations use expected market returns (e....
1
vote
0answers
22 views

Covariance time frequency

I have rolling 3-year returns for an asset and a benchmark. I want to compare the covariance of the asset and benchmark, should I use the covariance of the rolling 3-year returns or the covariance ...
1
vote
0answers
30 views

Hedging an option on a non-traded asset in BS world

I have given the following task given. Suppose you are in a Black-Scholes World where you have the standard assets $$ dS_t = \mu S_t dt + \sigma S_t dW_t $$ $$ dB_t = r B_t dt $$ and now you also ...
2
votes
0answers
31 views

Cointegration between prices and dividends. How do I get the following expression?

Actually, I have two questions: 1. Let us assume that expected returns are constant. Then, we have the following expression for how the prices should be determined, provided that the operators are ...
1
vote
1answer
28 views

Beta: Cumulative vs. Simple Returns

How would calculating Beta using cumulative returns differ from Beta calculated with monthly returns? Is one more appropriate to use than another? https://en.wikipedia.org/wiki/Beta_(finance)
-1
votes
0answers
15 views

Consider a single period security market with two assets. Assume the current prices are [on hold]

Consider a single period security market with two assets. Assume the current prices are s1(0)=1,s2(0)=2 There are two states at time one and the payoff matrix is A= ( \begin{matrix}1 & 1\\ 1 ...
1
vote
0answers
14 views

Black-Derman-Toy model AND European-type bond call option

In a Black-Derman-Toy model in which Ω ={ ω1, ω2, ω3, ω4 }, the risk-neutral probability for each state ωi, i = 1, 2, 3, 4 is 1/4 . The spot rates in BDT model are given as follows. ω r1 r2 ...
4
votes
1answer
284 views

Exposure calculation of a re-coupon swap

How to calculate the exposure of a recoupon swap (when the MTM of an i.r. swap is settled and the fixed rate is reset to the prevailing swap rate for the residual maturity). It's used to reduce the ...
35
votes
5answers
67k views

A simple formula for calculating implied volatility?

We all know if you back out of the Black Scholes option pricing model you can derive what the option is "implying" about the underlyings future expected volatility. Is there a simple, closed form, ...
2
votes
1answer
27 views

How to price a phoenix and snowball type autocallable options?

I'm currently studying the pricing of autocallable options, especially snowball (accumalated coupon) and phoenix (accumlated coupon, but the coupon may also be autocalled if the underlying price ...
1
vote
0answers
25 views

Which technique determines if var x1 leads var y? Assuming var x1 may need to be transformed

Suppose I want to predict future changes in variable y (stock price over time). I notice that variable x1, inverted and delayed three months, tends to lead y. Which technique can I use to find other ...
3
votes
1answer
2k views

How to tail a hedge? (Question 3.26 from Hull, edition 10)

I am new to finance so I apologize if my question is really basic (which it probably is). If this is not the right "stackexchange" group for this, kindly refer me to the right one. Let's say you own ...
2
votes
0answers
17 views

how to model NGARCH using 5min frequency data?

NGARCH model using 5-min High-frequency data in R I wanted to analyze some 5 minute frequency data of stock market. My teacher asked me to use NGARCH to model, but I didn't know how to program.Here ...
18
votes
4answers
16k views

What is a Heat Rate Option?

I tried a search with google but I can't find a clear definition of what a Heat Rate Option is. I would appreciate if someone could explain to me what this type of option is. My understanding is ...
1
vote
1answer
21 views

Anywhere to find historical float shares (or restricted shares) of US stocks?

I'm trying to collect the historical stock float data, but can't find it nowhere. We can easily find historical quarterly shares outstanding data in sec edgar, and we know that floating stock = ...
2
votes
0answers
29 views

Monte Carlo (resampling) in m.v. portfolio optimization

The instability and high sensitivity of optimisation results can be augmented by adding another layer of quantitative methodology in the form of Monte Carlo Simulation. The name Monte Carlo alludes to ...
2
votes
1answer
15 views

How would I develop confidence bounds for a function of 3 random variables, 2 of which are correlated?

I am tasked with developing confidence intervals for the function x = 1 - |(a+b)/c| where a, b and c are random variables. a and b are normally distributed, but c is heavily skewed left. further ...
3
votes
0answers
26 views

Does convexity in the IV space means convexity in the price space?

Let's assume that we only look at OTM options to construct a Risk Neutral Density (RND). As the RND is the second derivative of the price of the option with respect to the strike, we would expect ...
24
votes
12answers
12k views

Probability of touching

For a vanilla option, I know that the probability of the option expiring in the money is simply the delta of the option... but how would I calculate the probability, without doing monte carlo, of the ...
1
vote
1answer
359 views

API for fundamentals for NSE and BSE

I want APIs for accessing fundamental data of all stocks in NSE and BSE India. I have searched a lot But no luck. Any such services available please guide me. I'm looking for specifically quarterly ...
1
vote
0answers
26 views

Relationship between correlations of long only and short only portfolio with long-short portfolio?

I am working on one quality and value factor, the correlation between a long-only or short only portfolio of these two factors is respectively 0.7 and 0.8, and the correlation between combined long-...
2
votes
2answers
58 views

Carry & roll - question regarding the repo transaction

Could someone please explain the carry and roll trade that a lot of traders are doing with negative euro debt? I read an example that they borrow in the repo market then buy a longer dated bond to ...
1
vote
0answers
14 views

Relation between low rate and credit risk

In the Handbook of Fixed Incomes Securities, there is this part: The lower federal funds rate prods banks to be less aggressive in issuing deposits, such as certificates of deposits (CDs). Their ...
1
vote
0answers
30 views

PV01 of Physically settled Swaptions contrat

Can you please help me figure out how to find PV01 Physically settled Swaptions contract 20Y30Y with fwd rate 0.01974 with fixed freq=2, using ACT/360 with 02/08/2019 -> 02/08/2039 and 02/08/2069 ...

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