3
votes
1answer
75 views

compute technical indicators from candle data

i have a rookie question but can't find the answer anywhere so..what is the right way to compute a simple moving average when you have an array of (open,close,low,high) tuples ? From what i saw so ...
3
votes
1answer
156 views

Derivation using Ito's Lemma of price process

Define $q(t)$ as the log price minus a linear trend $$ q(t) = \ln P(t) - \mu t $$ Assume the log price process = Equation 1: $$ dq(t) = - \Theta q(t) dt + \sigma dW(t) $$ Can you show that the ...
3
votes
1answer
138 views

Asset pricing - Technology

I am working a bit on this paper, which is about Long-run risk through Consumption Smoothing. In equation (8) and (9) the authors define the stochastic process for the technology as: $$Z_t = ...
3
votes
2answers
152 views

American vs European Options on equity index options

I have a question regarding the usage of European vs American Options. According to Professional Risk Mgr Handbook 2010, American-style options are used mostly on equities whereas European-style ...
3
votes
2answers
119 views

Proving Derivative Property of Moment-Generating Function

In Shreve II, exercise 1.8, he walks the reader through proving the derivative of a moment-generating function $\phi$ is equal to the expectation $\mathrm{E}[Xe^{tX}]$; i.e., $$ \phi^\prime(t) = ...
3
votes
1answer
234 views

Why is CSA currency OIS rate used in discounting instead of local currency OIS?

I have been struggling to understand the logic behind cross currency OIS discounting (where cash flows happen in different currencies than the collateral is paid). I will illustrate my question ...
3
votes
1answer
153 views

Compare events effect on stock prices from different time periods

I’m going to test for the effect corporate credit rating announcements have on stock prices through different economic climates (good times vs. bad times). I want to research whether or not the stock ...
3
votes
2answers
83 views

Probability of Closing Stock Price Over a Defined Period

I found this equation when I was reading "Paul Wilmots on Quantitative Finance" which calculates the probability that of a stock price ending/landing on a particular price (S'). So if the stock ...
3
votes
1answer
80 views

Estimating $\mu$ - only increasing $T$ improves estimate?

Assuming an asset price $S$ follows a geometric Brownian motion (GBM), the log returns $R$ are distributed as $$ R_i := \log\left(\frac{S_i}{S_{i-1}}\right) \sim \mathcal{N}\left(\left(\mu - ...
3
votes
2answers
150 views

Extracting Default probability from a single CDS

I have to find the CDS's default probability using the simplest Poisson Process (intensity constant). I'm wondering how to get this estimate if I have only a CDS with maturity 5years. If I had ...
3
votes
1answer
175 views

What is the best data structure/implementation for representing a time series in C#?

I'm looking for a tick by tick high performance container. So far I've been using List where Tick is a simple struct with a DateTime and double field. I'm using Linq for date lookups but it's ...
3
votes
1answer
67 views

According to Lo and MacKinlay (1990), momentum profits can be divided in 3 parts. What do they represent exactly?

At first, Lo and MacKinlay (When are Contrarian Profits Due to Stock Market Overreaction?, 1990) didn't do it for momentum precisely. However,Kyung-In Park and Dongcheol Kim (Sources of Momentum ...
3
votes
1answer
96 views

Measure the effect of a natural disaster on a stock market index

I am very new to using stata and very new to using Garch models. I am currently doing my final dissertation for my MSc in Finance studies and regarding my topic I understood that i had to use garch to ...
3
votes
1answer
108 views

Accuracy of GARCH& ARCH forecast

I'm learing ARCH&GARCH model. I have four questions that I don't know the answers 1st: ARCH & GARCH are often used to evaluate equities. Does it mean that ARCH and GARCH are fitter for high ...
3
votes
1answer
187 views

How can one value a Bermuda option?

A Bermuda option allows early exercise at predefined dates, e.g. at maturity equal to $t_1$, $t_2$, $t_3$,...; hence , would its value be the sum of 3 discounted European options with 1-year ...
3
votes
1answer
223 views

Numerical example of how to calculate local vol surface from IV surface

I'm looking for an excel example (not a copy of Dupire's eqn) of how to convert an IV surface to a local vol surface. If unsuccessful I'll work through Dupire's eqn but would be helpful to look at an ...
3
votes
1answer
109 views

Boundary conditions of PDE from SV model with stochastic interest rate

The PDE for the American put option price $P(S,\sigma ,r,t)$ is \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + ...
3
votes
1answer
99 views

LIBOR with different tenor

Let $F(t;S,T)$ be the forward rate from $S$ to $T$ seen at time $t$, and $I$ be one of tenors, i.e. $I$ is one of {1M, 3M, 6M, 12M}. Then the forward curve $t\mapsto F(0;t,t+I)$ is $I$-forward curve. ...
3
votes
1answer
235 views

Value of European Call equals Value of American Call, Question on Explanation/Proof

I am reading S. Shreve, Stochastic Calculus for Finance, Vol. I. There he proves that American Call Options have the same value as European Call Options. In the proof he uses that for a Call option ...
3
votes
1answer
156 views

Negative Interest Rate & Basis Models

Since markets are showing negative interest rate, I'm forced to find a model that can catch this behaviour. Because of that, I have implemented and calibrated the G2++ (or the Hull-White 2 Factors) ...
3
votes
1answer
144 views

Distribution of Black Scholes call option price at time 0<t <T

Does anyone know how to find the probability law (distribution) under P* of a Black Scholes Call Option price $C_t$ for $0 < t < T $? (Under P*, $ dC_t = \frac{\partial c}{\partial s}\sigma S_t ...
3
votes
1answer
132 views

Combining modern portfolio theory and Kelly betting?

I'm using modern portfolio theory to compute the frontier of efficient portfolios. I'd like to pick the best one in the spirit of Kelly betting, ie. maximising expected growth. I'm looking for a ...
3
votes
2answers
216 views

Forecasting problem with Geometric Brownian Motion in Wolfram Mathematica

I'm a full time undergraduate student from Peru, and I'm trying to use the Geometric Brownian Motion example used in the help section from Wolfram Mathematica in order to forecast future stock ...
3
votes
1answer
70 views

the incremental value of Kelly Criterion under difference circumstances

I know that the Kelly Criterion maximizes bankroll, but i was wondering how much value it contributes to the total return and under what circumstances. I'm trying to understand the difference between ...
3
votes
1answer
236 views

Why is the volatility smile important

One thing I can't understand clearly is why there is so much focus on the volatility smile. Given my knowledge of the Black and Scholes model, this is what I get: People use the volatility smile as a ...
3
votes
1answer
599 views

Sortino Ratio calculation

I've been using an excel template to calculate the sortino ratio for my automated trading strategies. http://investexcel.net/calculate-the-sortino-ratio-with-excel Basically i input my monthly ...
3
votes
2answers
97 views

Time 0 value of an American Put in Cox-Ross-Rubinstein model

This is a question from a problem sheet which I have handed in and have solutions for. The only examples of this in class I have seen are examples where the interest rate is 0. "Consider a ...
3
votes
2answers
1k views

How do I calculate the PPP adjusted exchange rate between two countries?

I have been trying to calculate the PPP-adjusted EURUSD exchange rate. I am not sure if it is the same as relative PPP, for which I have used this formula: Spot rate at time t = Current spot rate * ...
3
votes
1answer
82 views

ETNs as bank funding

I've just read the article in the link below and would like to know if someone can elaborate on a statement. I have added the whole paragraph, but highlighted the part about the use of ETNs as cheap ...
3
votes
1answer
208 views

Why future (forward) volatility smile is important to path dependent option?

I was wondering why future volatility smile is important to path dependent option and American type option such as Bermudan swaption. It would be best if someone could provide a reference article as ...
3
votes
1answer
144 views

Simulating Brownian motion with jumps

I am trying to improve my understanding of jump processes. As a first step, I want to simulate sample paths for the process $$dX(t) = dw(t) + dJ(t)$$ where $dw(t)$ is a Brownian motion and $dJ(t)$ ...
3
votes
1answer
791 views

What is the difference between a benchmark yield curve, funding curve and a basis spread curve?

I am trying to understand why these curves are important, and what they are used for in the industry today (if not at all).
3
votes
1answer
133 views

What are recent important papers on credit portfolio risk modeling?

I'm interested in papers which consider mathematical models of risks of different portfolios of retail credit. This is not my area of research, so I may be misusing some terms. The idea is simple: I ...
3
votes
1answer
75 views

What is the difference between a book value and a market value?

0 down vote favorite I would like to understand the following problem. A 2yr zero-coupon bond has an annual yield rate of 11% per year. A 4yr zero-coupon bond has an annual yield rate of 19% ...
3
votes
1answer
268 views

Portfolio choice problem of a CARA investor with n risky assets

Ok, I am working on a problem that consists of the following: I am looking to solve the portfolio choice optimization problem (maximizing utility with a known utility function) in the case where all ...
3
votes
2answers
107 views

arbitrage opportunity in a two period model

I have a little problem evaluating an european call. I Suppose the following: in $$t=0 : S_0 = 10$$ $$t = 1 : S_1 = \{10,11\}~with ~p=0.5$$ riskless rate : $(1+r)=\beta=1.049$ Strike ...
3
votes
1answer
107 views

When are implied and real world parameters the same?

Suppose $T$ the maturity of a risky bond which defaults with probability $p$ over its lifetime. If it defaults it pays zero. Thus to price this bond in risk neutral terms would give ...
3
votes
1answer
100 views

In Dupire's paper, why is $(S_t, t)$ in the $(K, T)$ space?

I'm new to local volatility model. From Dupire's paper and most of the textbooks, they derived the local volatility $\sigma(K, T)$ in the $(K, T)$ (i.e., strike and maturity) space, from call prices ...
3
votes
1answer
55 views

Swapping expectation operator with differential operator

Suppose I have a general SDE $dx_{t} = \mu dt + \sigma dz_{t}$ Then I can put $E[]$ on both sides to get $E[dx_{t}] = E[\mu dt] + E[\sigma dz_{t}]$ Now comes the question: I've seen some formulas ...
3
votes
1answer
74 views

Longevity risk modelling

What is Longevity risk, and how to model it under DC and DB pension plans? characters|characters|characters|characters|characters|
3
votes
1answer
186 views

Normalized price process $Z(t)=\frac{\Pi(t)}{B(t)}$

If an interest rate model with the following $P$-dynamics for the short rate. $$dr(t)=\mu(t,r(t))dt+\sigma(t,r(t))d\bar{W}(t)$$ Now consider a $T$-claim of the form $\chi = \Phi(r(T))$ with ...
3
votes
1answer
291 views

Bayesian or Frequentist in Finance?

I'm currently an undergrad at a Canadian university and our finance courses has been brought up through the frequentist approach (ols, hypothesis testing, sampling theory). Only recently, through ...
3
votes
1answer
314 views

Stochastic Volatility CIR estimation

Would anyone have a code (pref. Matlab or R) for any type of estimation (QML, GMM) not using option prices of a stochastic volatility model driven by a CIR process described below? \begin{equation} ...
3
votes
1answer
65 views

Why Beta Distribution for Credit Migration

When modelling credit migration probabilities (e.g. AAA to AA), research has indicated the use of the Beta Distribution simply because it fits empirical data. My question is; What are some other pros ...
3
votes
2answers
355 views

How to find the best fitting GARCH model for a portfolio composed of 3 ETFs in R?

I am doing a project for my class Financial Time Series in which I am trying to forecast my portfolio log returns using a GARCH fit. I am having a bit of trouble determining the best way to fit this ...
3
votes
1answer
109 views

Maximizing utility subject to a wealth constraint

Let $\tilde{E}$ be the risk neutral expectation, and $X_t$ the wealth that time t and $R$ the return of a risk-free investment. Consider maximizing the function $EU(X_N)$ subject to ...
3
votes
2answers
137 views

Why can't I multiply two SDE Solutions?

SDE 1 is S1 = S10 exp( (r1-sigma^2/2) * dt + sigma dW1 ) S2 = S20 exp( (r2-sigma2^2/2) * dt + sigma2 dW2 ) E[dW1 dW2] = rho I want to price an option on S1 x S2 I know I need to use the SDE's to ...
3
votes
3answers
139 views

GARCH parameters

I'm trying to estimate parameters of GARCH(p,q) model. I tried p=1, q=1 with t-distribution errors. Ljung-Box showed no correlation in residuals and squared residual. But the null hypothesis that ...
3
votes
1answer
88 views

Binary option expression

Given r=0, σ(K)=const Binary=lim┬(ε→0)⁡〖((C(K,σ(K))-C(K+ε,σ(K+ε))))/ε〗 What is the analytical expression for the binary option value? σ(K)=const Therefore, Binary=lim┬(ε→0)⁡〖((C(K)-C(K+ε)))/ε〗 ...
3
votes
1answer
485 views

How trading in currency pair works, underlying techniques and mechanisms

I am somewhat experienced in Forex trading, but I have a question which has bothered me for quite some time. If we for instance go back in time four months, to before the beginning of value loss the ...

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