0
votes
2answers
90 views

Solving for r in the Black Scholes equation

Could you please correct which parts of my reasoning are wrong? Let's suppose that I know for sure that my estimate for a stock volatility is right (I have a crystal ball) and that it will be for ...
1
vote
1answer
54 views

Expected Value of Products of Processes

Suppose I have two processes. $A_t = A_0 \exp((a-\frac{1}{2}\sigma_A^2)t+\sigma_A W_t^A$ $B_t = B_0 \exp((b-\frac{1}{2}\sigma_B^2)t+\sigma_B W_t^B$ I would like to calculate $E[A_s B_t]$ where s ...
1
vote
1answer
33 views

Calculation loan's margin from bank perspective

I was wondering how bank calculates in practice the amount of money it earns after granting a credit (I hope margin is the proper word). Supposing, that the client took 3-year 10000 euros loan (36 ...
1
vote
1answer
69 views

FX Modeling references

I would like to have some sugestions of reference books on FX modeling with strong mathematical approach, preferably combined with market pratictioner quant perspective. All sugesting are welcome! ...
1
vote
1answer
72 views

How to statistically prove that an automated trading strategy outperforms the market? [closed]

For a university project, I have been working on a rather complex automated trading strategy, that levers machine learning techniques. I backtested the algorithm, as a result I have daily return data ...
1
vote
1answer
185 views

Volatility Smile Approximation

Does anyone know what type of model is used to model the skew and IVs inside Thinkorswim platform for its volatility smile approximation? I am trying to replicate but do not know where to start. Any ...
0
votes
0answers
28 views

American call early exercise, considering a portfolio

Im aware there are lots of questions about this, but I am interested in a particular method of showing why an american call (with no dividends) should not exercised early. Here is the text I'm ...
0
votes
1answer
53 views

Ho-Lee model - A and B derivation for $P(t,T)=e^{-A(t,T)-B(t,T)r_t}$

I am analyzing the transition of the bond prices in the affine models in the form of $P(t,T)=e^{-A(t,T)-B(t,T)r_t}$ using the property that the diffusion and the drift of an affine model can be ...
0
votes
1answer
38 views

When is option value inversely related to expected volatility?

It is common knowledge that the greater the expected value, the higher the option value. However, there are surely exceptions, as written by Paul Wilmott's FAQs in Quantitative Finance Q: If you ...
-1
votes
1answer
42 views

Determining confidence level of directional signals

With regards to technical analysis, are there ways of determining the confidence level of a directional signal? Taking a relative strength index (RSI) as an example, can the extent to which an asset ...
0
votes
1answer
35 views

Quantum Computing for Quantitative Finance

It's been a while that quantum computing is looked as the next step in computational science. I somewhat always tought we were decade aways from it's happening but it appears I was wrong: ...
0
votes
0answers
10 views

How to reduce variance of mean reversion estimator with maximum likelihood?

I estimate the parameters of an Ornstein-Uhlenbeck process with Maximum Likelihood. The mean reversion speed estimator is well known to be biased. There are methods to reduce the value of the expected ...
1
vote
1answer
49 views

Discount factor taking into account yield curve shape

I have always been told that the discount factor formula is just: $$ DF(T) = \frac{1}{(1+L_{t_0})^T} $$ where $L_{t_0}$ is the LIBOR rate on one period (the first one I guess) and $T$ the number of ...
1
vote
1answer
29 views

ATM volatility and flat volatility

Why do the implied volatility curve and the flat curve cross over the ATM volatility (at 100%) ? Tx
1
vote
1answer
40 views

“Expectation” of a FX Forward

I have an FX process $X_t = X_0 \exp((r_d-r_f)t+ \sigma W_t)$. Now clearly $E[X_t] = F_{0,t}^X$. i.e. a forward contract of the process $X$ starting at time 0 and maturing at time $t$. What if I ...
-1
votes
0answers
17 views

How to find loans for investor collateral

I got this asssigment: Company A lends 20 mil from investor and has to put up investment collateral of 30 mil worth of loans. Company A operates in underwriting business. Collateral loans have to ...
0
votes
0answers
22 views

Why do people use weighted regression with returns?

For example, by ADV. Intuitively it makes sense that a very liquid high ADV stock should carry more weight, but when I try it with some real life data I get higher standard error than unweighted...is ...
4
votes
0answers
90 views

How to trade the Ornstein-Uhlenbeck process?

My question comes from this paper, which is a short version of Avellaneda's paper The picture bellow provides a summary of the equations. Do I understand correctly that in order to trade OU process ...
1
vote
2answers
81 views

How to show that the exponential Vasicek model is not an affine term-structure model?

From the pricing formula, we know that the value at time $t\in [0,T]$ of a zero coupon bond maturing at time $T$ is $$ B(t,T)=E\left(\exp{\left(-\int_{t}^{T}r_sds\right)}\bigg|\mathcal{F}_t\right). ...
1
vote
1answer
53 views

Vasicek model problem

I am analyzing a problem where the below is given Vasicek model with risk-neutral dynamics $$dr_t = \kappa (\theta - r_t)dt + \sqrt{r_t} dW_t \quad \quad (1) $$ bond prices ...
0
votes
1answer
50 views

trading equities on options feed/microstructure data

Obviously, not asking for a trading strategy, but do people successfully use options feed/microstructure data to trade equities intraday? What's the general framework for such strategies?
1
vote
0answers
34 views

Modelling log-returns and calculating the portfolio return

I know this might be a trivial question, however, I would be grateful for some clarification. I am working on weekly log-return data, doing volatility-foracasting using GARCH models and then using ...
0
votes
1answer
38 views

Andersen Broadie American/Bermudan Put

I'm trying to implement Andersen and Broadie's dual method for an upper bound (here) of a regular American Put. I understand the process to compute it, but I have a conceptual issue : everything ...
3
votes
1answer
89 views

Girsanov Theorem for Quanto/Compo adjustment

Assume that I have a foreign asset $$Y_t = Y_0 \exp \left((r_f-\frac{1}{2}\sigma^2_Y)t+\sigma_Y W_t^1\right)$$ and an exchange rate $$X_t = X_0 \exp\left((r_d-r_f-\frac{1}{2}\sigma^2_X)t+\sigma_X ...
7
votes
2answers
440 views

Do efficient market hypothesis and random walk theory convey the same concept?

According to investopedia efficent market hypothesis is The efficient market hypothesis (EMH) is an investment theory that states it is impossible to "beat the market" because stock market ...
1
vote
1answer
55 views

Option delta - Conditional probability definition?

Can someone help me interpret this definition of delta? Delta is a conditional probability of terminal value (St) being greater than the Strike (X) given that St > X for a call option. Is the ...
1
vote
1answer
71 views

Quanto/Compo adjustments - Product of two geometric brownian motion

Let's say I have two processes $X_t =X_0 \exp((a-\frac{1}{2}\sigma_X^2)t +\sigma_X dW_t^1)$ and $Y_t=Y_0 \exp((b-\frac{1}{2}\sigma_Y^2)t +\sigma_Y dW_t^2)$ and I then multiply them together (like ...
0
votes
0answers
9 views

model to predict variable evolution [migrated]

Suppose that I have a set of variables X1 X2 and X3 that explain the evolution of a ...
0
votes
0answers
18 views

Quantlib xll - Converting deposit/swap curve to zero curve

I am trying to create a spreadsheet using the Quantlib xll to convert deposit/swap rates to zero rates. I tried to implement such by referencing to the C++ code listed here: How to sum interest rate ...
1
vote
1answer
26 views

Why NYSE is not included in TAQ data for NASDAQ listed companies?

I am using TAQ data to see from which exchanges bids (or asks) are coming. I have got this for AAPL (Apple company, listed in NASDAQ) for a sample day: ...
0
votes
0answers
11 views

Daycount Actual/Actual AFB example

This question is about the following example in Wikipedia about time factor using the Actual/Actual AFB daycount. Assume that the $t_1=\text{28 Feb 2004}$ and $t_2=\text{29 Feb 2008}$. There are ...
0
votes
1answer
39 views

SABR Calibration: Normal vs Log-Normal Market Data

This question is about getting some clarification as to how to understand market quotes for normal & log-normal vols together with certain model assumptions. So let us define ...
0
votes
0answers
45 views

approximating fBm stochastic integral

Suppose I have the following stochastic integral: $$\int_a^b f(t)dB_H(t)$$ with the term $dB_H(t)$ a fractional brownian motion with associated $H$ parameter. Is it true that for $H \in (1/2,1)$, ...
1
vote
0answers
54 views

How to choose a GARCH model which delivers iid standardized residuals?

For my thesis I first need to examine nine financial time series and fit a conditional volatility model such that the obtained standardized residuals ($z_t = \epsilon_t / \sigma_t$) are approximately ...
5
votes
2answers
156 views

Where to find good notations to teach investment portfolio maths?

I don't know whether this question is in order here. I do a bit of teaching and I am preparing my own notes but I thought that his should not be necessary. In which book/pdf on the web can we find a ...
0
votes
2answers
76 views

Accuracy Rebonato Swaption Approximation Formula among Different Strikes

Can somebody explain me if the Rebonato swaption volatility approximation formula is accurate for only ATM strikes, and if yes why? Can it also be used for ITM and OTM strikes? My foundings: Let $0 ...
5
votes
2answers
88 views

Is the money market account (MMA) numeraire and the forward measure equivalent?

Suppose we have a risk-neutral measure $\tilde{\mathbb{P}}$. The money market account is given as $M(t) = e^{\int^t_0 R(s) ds}$, while the price of the zero-coupon bond at time $t$ that matures at $T$ ...
0
votes
0answers
18 views

RWA Calculations Formulae

I am working as IT developer for one of the investment bank and I have recently joined and it is completely new domain to me. While I am still learning about this domain, what I was looking for short ...
2
votes
1answer
39 views

Need advice about distributed backtesting architecture [closed]

We are working under complex enough distributed trading system where several components will run on different physical machines. Unfortunately, I'm stuck on part backtesting part. Originally we was ...
0
votes
1answer
42 views

How to determine portion of portfolio's risks from components?

Say I have a portfolio of 3 stocks $A,B,C$ with $\mu_A = 5%$, $\mu_B = 10%$, $\mu_C = 15%$ and volatility $\sigma_A = 10%$, $\sigma_B = 15%$, and $\sigma_C = 25%$. Let us also say that correlations ...
0
votes
0answers
30 views

Adding negative EV position to portfolio for diversification?

Say I have a portfolio of expected return $10%$ and volatility $20%%. If I have another asset that is either one of: Negatively correlated Positively correlated Uncorrelated With negative expected ...
3
votes
0answers
49 views

On the reflection of a stochastic integral

Let ${(I_t)}_{t\geq 0}$ be a stochastic integral defined by $$ I_t=\int_{0}^{t}\theta_sdW_t, $$ where $W$ is a standard Brownian motion defined on $(\Omega,\mathcal{F},{(\mathcal{F}_t)}_{t\geq ...
2
votes
3answers
51 views

What does it mean for an option strategy to be leveraged

Probably a newbie question, but what do traders mean when they say that an option strategy is leveraged ? And when can we say that it is the case ?
0
votes
1answer
60 views

Mathematically: How does increasing the number of assets reduce idiosyncratic risk?

As part of an Asset Pricing Module I'm currently taking, whilst looking at APT Ross (1974), we looked at how according to this model, risk originates from both systematic and idiosyncratic asset ...
0
votes
1answer
35 views

How can I compute zero coupon bond prices from dirty/clean prices of coupon bonds?

I am having problems with computing zero-coupon bond prices. The question is the following: Today is $t$=14.4.2016 and I know dirty and clean prices of coupon bonds expiring at maturities: 4.7.2016, ...
0
votes
0answers
22 views

How to fit model implied forward curve with market forward curve for Ornstein-Uhlebeck?

I have a spread option model of 2 correlated Ornstein-Uhlenbeck commodity prices that I estimate the parameters of with Maximum Likelihood. What is the formula for introducing the additional ...
3
votes
2answers
32 views

The relation between exchange rate SDE and respective interest rates

The exchange rate between a domestic currency money market and a foreign currency money market can be expressed as $$ dQ(t) = (r_d - r_f)Q(t)dt + \sigma Q(t)d\tilde{W}(t) $$ where $r_d$ is the ...
3
votes
0answers
60 views

Interpolation of forward zeros-coupons bonds simulations for missing maturities (ESG data)

I have a set of economic scenarios simulated with Barrie and Hibbert ESG. The stochastic model for interest rates used is Libor Market Model Shifted. I am facing a problem with zeros-coupons prices. ...
0
votes
1answer
19 views

short selling with collateral accounting

I don't know how the accounting works for short selling with collateral: For example if a stock is \$10 a share and turn out to be $15 a share a week later. At time 0, you borrow and sell 10 shares ...
1
vote
0answers
17 views

Calibrating and simulating returns from a t-distribution

A slight twist (I hope) on the familiar problem of simulating log returns from a t distribution. My two questions concern calibration to sample data. First, one can infer the degrees of freedom in the ...

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