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1answer
77 views

Delta and vega sensitivities for Cap

I have a task to do but it is very difficult.. I have to calculate the: Delta Sensitivity analytically, that is the first derivative of caplet price wrt the forward rate, using the black model to ...
0
votes
1answer
54 views

What does XIRR show?

I've put aside 1000 EUR for trading strategy test. Made number of trades where each position was worth 5 EUR. At any moment there was invested from 0 to 80 EUR. Entered all cashflows to XIRR function ...
0
votes
0answers
18 views

Find the stock exchanges a security is traded in given a CIK?

I have all the CIKs and relative tickers of all the traded securities that I need (https://www.sec.gov/include/ticker.txt). My question is: How do I find the stock exchange that a gives security is ...
-3
votes
1answer
53 views

Calculation of monthly interest and capital repayment in a variable rate mortgage

In my exercise, I take out a 240,000€ mortgage from a bank which I pay off over a period of 30 years. The interest rate is a market index plus a spread. Initally the market index is 1% and the spread ...
2
votes
1answer
151 views

Confusion about terminology : Finite difference for option pricing

Consider the following initial-boundary value problem for $u = u(x,t),$ $$u_t - a u _{xx} = f(x,t) \text { for } 0 < x < L \text { and } 0 < t< T$$ along with bunch of initial and boundary ...
0
votes
0answers
36 views

Which exact interest rate should I use for valuing equity index futures (ie. SPX, MXEA)?

I'm trying to build a model that values futures for equity indicies like SPX. For example, this product link here. I know that the model is simple (please correct me if I'm wrong): $$ S_{T} =S_{0}e^{(...
-1
votes
1answer
41 views

Confusion about candlesticks colors [closed]

Why is the second green candle stick green? Given that its closing price is less than the previous candlestick's closing price, shouldn't it be orange? Source: coninbase 1m chart for ethereum: https://...
-1
votes
1answer
42 views

Portfolio variance $<=$ weighted average of individual variances [closed]

In portfolio theory, I often (with some justifications but the message is the same) come across the following statement: "The most important quality of portfolio variance is that its value is a ...
3
votes
0answers
56 views

FX Option Price Quotation

I'm trying to replicate the following FX vanilla option pricing exercise (and the conversion between the quote types), taken from Wystup (2006). A call's value today is well-known given by BS / ...
0
votes
0answers
25 views

how to get 3 month Forward rates from Hull white model simulation?

I implemented the Hull White one factor model in Monte Carlo simulation, and got the short rate on each node (time step =1month). my question is how to get the forward rate from the short rate? I am ...
1
vote
0answers
28 views

Brinson attribution for arbitrary set of style factors (size, momentum, vol, etc)

I'm looking to do a Brinson performance attribution on a portfolio of stocks where instead of decomposing the returns in terms of sectors we use factors instead. Basically, I want to do what Style ...
-1
votes
1answer
84 views

How to show that a Brownian motion is normally distributed and that the covariance is zero?

I need help under standing this question. So i have the following given the logarithm of the price of a share of stock is given by \begin{align*} p(t)=p(0)+\mu t+\sigma W(t), \quad t \in[0, T] \end{...
0
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0answers
30 views

Extrapolating curve

Let say I have few discrete points for Discount factors and I want to create a continuous curve for interpolation and extrapolation at custom dates. I was told that,...
-1
votes
1answer
25 views

Value at maturity of long position in money market

This should be easy, but for some reason I am struggling with it. Say you have a long position in the money market (you hold dollars), say you own a quantity of $Ke^{-r(T-t)}$ dollars at time $t$, ...
0
votes
0answers
41 views

cvxpy sparse portfolio optimization with lasso under constraints

I want to solve a sparse optimization problem with cvxpy. This is a lasso regression under constraints. The lasso regression is basically composed of the well-known OLS term (MSE) and the L1 norm. The ...
0
votes
2answers
125 views

Backtesting a portfolio strategy with several assets

I am aware that there exist several libraries and programs that allow to baktest a portfolio strategy by iterating through the OHLC dataframe of the stocks of interest (Backtrader, Backtesting, ...). ...
0
votes
1answer
49 views

IRR with Inflation Rate

I have cash inflows and cash outflows for a 7 year period and my MIRR and inflation rate. That's all the information I have. How do I calculation the IRR taking the inflation rate into account in ...
0
votes
0answers
30 views

Leakage and bias in XGBoost trading strategy

I apologize for my persistence, i'm on a course of study and doubts increase every day. My goal is "just" to code a profitable forex trading strategy with machine learning. I'm trying to ...
-1
votes
1answer
123 views
+100

'Optional Early Termination' clause

For market practitioners such as swap traders out there: in your experience, does the below clause when bilateral is similar to a difference between European and <...
0
votes
0answers
28 views

What is the name of leverage contracts where the worst case payoff is zero?

In a typical leverage futures contract the value of a position can be negative. That is to say, if you go long \$100 with 10x leverage at a price of \$50 and you then sell at \$40, the value of the ...
8
votes
2answers
233 views

ETF Market Making - Locking profits via hedging

I am interested in deeply understanding the way ETF market makers operate to profit. I already know that market makers profit from buying at the bid price and selling at the ask price, and I am also ...
1
vote
0answers
16 views

How to find the equilibrium price in a CDA with limit orders?

I'm trying to understand how a continuous double auction works, by working through the below setup: I'm trying to figure out what the final results would look like how to determine the equilibrium ...
0
votes
0answers
32 views

How to deal with blank entries in computing log growth

I am conducting a study to discover which variables best explain stock volatility during COVID. I am currently completing linear regressions before implementing GARCH, however I have come across a ...
0
votes
0answers
44 views

How to price barrier options under Black-Scholes?

I am looking for a rigorous proof for the closed form of the price of a barrier option (up-in/up-out) under Black-Scholes model, that is a step by step solution of the solution of the heat equation ...
2
votes
0answers
33 views

Understanding Bayes Rule of conditional expectation

Let $\mathcal{F}$ be a $\sigma$-algebra, $P$ and $Q$ be equivalent martingale measures and $\frac{dQ}{dP}$ the Radon Nikodym Derivative. I learned that $\Bbb{E}_Q[X]=\Bbb{E}_P[\frac{dQ}{dP}X] $, which ...
0
votes
0answers
51 views

Optimal withdrawal rate based on alpha and drawdown

My trading returns is about 50% monthly(alpha) and maximum drawdown is about 20%. Is there a mathematical way to define the optimal withdrawal rate X%(say when profit level reach y%) to avoid risk of ...
0
votes
2answers
117 views

Black Scholes implied vol of SVJ model

Under the SVJ model https://en.wikipedia.org/wiki/Stochastic_volatility_jump, what is the formula of the Black Scholes (log-normal) implied vol for an option with strike $K$ and time to maturity $T$ (...
0
votes
0answers
113 views

Bug found in Optimal Number of Clusters algorithm - from de Prado and Lewis (2018)

I believe I have found a bug in Optimal Number of Clusters (ONC) from the paper "Detection of False Investment Strategies Using Unsupervised Learning Methods". ...
0
votes
1answer
56 views

Corwin-Schultz estimator of bid-ask spread

I am reading a paper "A Simple Way to Estimate Bid-Ask Spreads from Daily High and Low Prices" cf.A Simple Way to Estimate Bid-Ask Spreads from Daily High and Low Prices The authors proposed ...
1
vote
1answer
63 views

Simulating exponential Vasicek/Ornstein-Uhlenbeck

I am trying to simulate commodity prices using the exponential Vasicek/Ornstein-Uhlenbeck model from Schwartz 1997 p. 926 Equation (1). I am using the closed form solution from Vega 2018 p. 5 Equation ...
0
votes
1answer
56 views

What was the probability distribution used for Mortgage Backed Securities (MBSs) during the subprime crisis?

The probability distribution used for mortgage backed securities divided them into tranches. If tranch#1 was worth 10 million USD, they got paid in full while the rest got paid partially. Most of them ...
0
votes
0answers
52 views

Machine/Deep Learning for Exotic Option Pricing - Reference Request

Exotic options, in general, have very time-consuming valuation models. I believe in recent years there has been some research done on using supervised machine/deep learning to predict the valuation ...
0
votes
0answers
22 views

Price of a zero coupon and fisher Weil duration

Suppose that the spot rate curve (continuously compounded) is 2% for t less than or equal to 9 years, and the forward rate f(9,t) is 7% (continuously compounded) for t > 9 years. Suppose you have ...
-1
votes
1answer
31 views

Total return of a bond using spot rates

Suppose that the current spot rate curve (annually compounded) is s1=0.2%, s2=0.8%, s3=1.2%. Assume that one year from now, the spot rate curve will be s'1=0.8%, s'2=1.4%, s'3=1.8%. Consider a 3-year ...
0
votes
1answer
44 views

PCA on returns gives negative loadings on market short

I have run a PCA on some returns to get a set of factors. All is good except that the first PC seems to be the short of the market, it has a correlation of -0.9 with the S&P500 but all the ...
4
votes
0answers
76 views

Pricing of strange Asian lookback option with European-style payoff $\max\{ \max_{u\in[0,T]}S_u-\frac1T\sqrt{\int_0^TS_t^2\mathrm{d}t},0\}$

I am trying to price the Asian lookback option at time $t$ with time-$T$ (European) payoff $\max\{M_T-A_T,0\}$, where $$M_t=\max_{u\in[0,t]}S_u,\quad A_t=\frac1t\sqrt{\int_0^tS_u^2\mathrm{d}u},$$ and $...
0
votes
2answers
60 views

Black Scholes informal derivation - question about a term in the equation

I am wondering what the term S means in the equation I have circled? I am not sure how to interpret it.
1
vote
1answer
65 views

Calculating vega in Heston?

I often see Vega in the Heston model specified as: \begin{align*} \nu & = \frac{\partial C}{\partial v} = \frac{\partial C}{\partial v_0} 2 \sqrt{v_0} \end{align*} where $v = \sqrt{...
1
vote
4answers
62 views

corporate bonds - general questions [closed]

Newbie here and not trading IRL but for a school assignment. I want to buy corporate bonds because they are a safe bet from what I read. I have a few questions though, I hope I will find an answer ...
1
vote
1answer
54 views

Binomial Pricing Model d and u

In the binomial pricing model, why do the magnitude of the up factor $(u)$ and down factor $(d)$ have to be multiplicative inverses? I have read from multiple sources that the reason for this is that ...
1
vote
1answer
81 views

What is the difference between log volatility and simple volatility in a GBM? [closed]

What difference do they make? Why do many people seem to find more accurate simulations with log volatility? standard volatility in GBM is defined as $\sigma = \frac{1}{N}\sum_{i=1}^N(x_i-\mu)$ where $...
0
votes
1answer
60 views

PCA and K-means clustering on returns

I am running a PCA on a set of returns and I would like to cluster the results of the output to group stocks that have similar factor exposures. However when I run the PCA on the covariance of the ...
-2
votes
0answers
35 views

Price of the inverse- floater

Suppose a 10-yr 4.3% coupon bond has a price of 100.7% of face, and a 10-yr zero coupon bond has a price of 61.9% of face. What is the price (to nearest 0.01, with $ 100 face) of an inverse floater ...
0
votes
2answers
125 views

Construct a zero coupon bond

Suppose a 3% 10-year bond is trading at 89 and a 7% 10-year bond is trading at 97. Then (assuming no arbitrage) the price of a 10-year zero-coupon bond would be: The answer should be 83. How using ...
0
votes
0answers
52 views
0
votes
0answers
63 views

Options Arbitrage

I have a basic question regarding the BSM formula, would be thankful for any assistance. As far as I understand $N(d2)$ and $N(-d2)$ stand for the probability of a Call and Put respectively being ...
1
vote
1answer
56 views

Correlation between assets used for valuing multi-asset options (Rainbow options, basket options etc.)

Is there an equivalent to implied volatility used when it comes to modelling correlation in option valuation for multi asset options such as rainbow options (best-of/worst-of calls/put), or is the ...
2
votes
1answer
39 views

How to find the price variance of an infinitely expanding Binomial Tree?

How to find the price variance of an asset in a Binomial Tree Model? Suppose the price of the Stock is $S_t$ at time $t$ and it has a probability of $p$ that will go up $u$ times to $u \cdot S_t$ and ...
0
votes
0answers
49 views

First Principal Component Large Volatility

I am conducting PCA on several return series of funds and am finding that when I look at the first principal component the values are huge and this the volatility is also enormous relative to the ...
4
votes
1answer
110 views

How much does a rise in volatility in a short-term option affect a longer-term option

How would a rise in implied volatility on a short-term option affect the implied volatility of another short-term option with the same strike, but with slightly-longer expiry? Assuming that the short-...

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