4
votes
1answer
74 views

How to express the volatility of two correlated Ito processes $Wt_1, Wt_2$ expressed in terms of $W_t$?

Having two correlated Ito processes ($W_t^1$ and $W_t^2$ are correlated Brownian motions with correlation $\rho$) $dX_{t} =\mu_{1} dt + \sigma_1 dWt_1 $ $dY_{t} = \mu_{2} dt + \sigma_2 dWt_2 $ ...
0
votes
0answers
24 views

Convert 90-Day Tbill to risk free rate on continuous basis

I am trying to use the BS formula to compute the value of a call option. To do that I need the risk free rate on a continuous basis. As far as I know, people typically use the 90 day TBill as a proxy ...
1
vote
1answer
77 views

2 Ito processes - $d(X_{t} + X^{'}_{t})^2 = (Y_t + Y^{'}_{t})^2 dt$ why it is true?

Having two Ito processes $dX_{t} =z_{1} dt + Y_{t} dB_t $ $dX^{'}_{t} =z^{'}_{1} dt + Y^{'}_{t} dB_t $ I am analyzing a proof of the product rule $d(X_t X_t^{'})=X_t dX_t^{'}+ X_t^{'} dX_t + ...
1
vote
1answer
25 views

arbitrage proof question

prove the condition $D<R<U$ is equivalent to the absence of arbitrage: R = risk free investment rate of return. U and D are returns corresponding to the upward/downward price movements of a ...
0
votes
1answer
31 views

how to measure a event driven strategy?

How to measure an event driven investment strategy? Say I have a strategy which I assume that if a firm has positive momentum and it has a refinance corporate action, it's value will increase. For ...
0
votes
0answers
24 views

Hull white tree and the pricing of an interest rate swap

Currently, I have been able to set up the hull white tree. To price the swap, and we use the formula from Wilmott "Introduces Quantitative Finance", where we use the discount factors for all ...
1
vote
1answer
27 views

Finding rate of return of bond sold before maturity

You purchase a bond today for $980; M=$1000, the coupon rate is 4% paid semi-annually, and there are n=7 years to maturity. If you sell the bond for $1025 in six months time, what is your rate of ...
0
votes
0answers
10 views

Exchange ratio (stock swap ratio) during a merger/acquisition

Good morning to all, The question is homework-related but I've done the research already. The task is to guesstimate how much money will a known company A pay if it wants to acquire the known company ...
0
votes
1answer
31 views

Excess, Residual and Active Return

in CAPM. What's the difference between these different types of returns? Active return Excess return Residual return
3
votes
1answer
60 views

Why can a swap option be regarded as a type of Bond option?

Why can a swap option be regarded as a type of bond option? My idea: Suppose the swap rate of the swaption is $s$. Now consider a bond option expiring at $T$ with strike, $(P_K)_t = ...
0
votes
1answer
21 views

Pricing foreign currency bonds - which approach is more theoretically “sound”?

You own a fixed rate corporate bond in foreign currency (let's say JPY). Your domestic currency is USD. Which of the these two approaches do you consider theoretically better? Discount JPY cash ...
0
votes
0answers
12 views

Black-Sholes call value as a function of Company’s Spot Price S-Option Driven [closed]

Consider a call option on ABC Inc. with the following information: Strike price $1 Maturity: 1 year Volatility: σ Interest rate: 0% No dividends. Let c(S) be the Black-Sholes call value as ...
-2
votes
0answers
11 views

Modeled as the driftless geometric Brownian motion with instant increments [closed]

Consider a stock S currently trading at price S0. The future evolution of the stock price (St) t≥0 is modeled as the driftless geometric Brownian motion with instant increments: dSt = σStdWt, where ...
0
votes
0answers
11 views

A generalized Brownian motion [closed]

A company’s cash position, measured in millions of dollars, follows a generalized Brownian motion with a drift rate a=0.1 per month and a volatility rate b = 0.4 per month. The initial cash position ...
1
vote
1answer
46 views

Isn't Black's approximation for American options inconsistent?

I have came across a formula suggested by Fisher Black (Fact and fantasy in the use of options, FAJ, July–August 1975, pp.36) for approximating the price of an American call written on a ...
3
votes
1answer
28 views

What is the effect of mean-reversion on an upper barrier knock-out call option?

Consider a mean-reverting normal model for an underlying $dX^{(1)}_t=-\kappa X^{(1)}_tdt+\sigma^{(1)} dW^{(1)}_t$, for fixed time-independent constants, $\kappa$ (mean-reversion) and $\sigma^{(1)}$ ...
3
votes
1answer
44 views

Solve Black scholes PDE without using any transformation

I know that one of the methods of solving the black scholes PDE given by : $\frac{\partial V}{\partial t} + \frac{\sigma^2 S^2}{2}\frac{\partial^2V}{\partial S^2} + rS\frac{\partial V}{\partial S} -rV ...
0
votes
1answer
23 views

What does it mean when a risk reversal is near choice?

I'm currently reading Kathy Lien's 'Day Trading and Swing Trading the Currency Market' and I came across this phrase on risk reversals: "near choice". What does it mean when risk reversals are near ...
0
votes
0answers
16 views

Fitting Copula and Simulation

I would greatly appreciate any insights into the problem described below, regarding using the data obtained from applying the functions of the 'rugarch' package into those from the 'copula' package. ...
3
votes
3answers
57 views

Are smart beta and risk parity the same?

So from what I have been reading online, smart beta ETFs aim to use a different type of weighting (instead of by market cap as traditional ETFs like SPY do to track an index) to achieve positive ...
0
votes
1answer
42 views

Payoff of option

Consider the payoff $g(S_T)$ shown the figure: I believe the payoff represented as a linear combination of the payoffs of some options with different strike and same maturity $T$ is $$g(S_T) = ...
1
vote
1answer
28 views

Pricing a Vanilla swap between coupons; What rates to use?

Vanilla Swap question. Entered into a 5Y fixed for floating HUF swap. Fixed is annual coupons, Float is semi-annual coupons. 1 month later I want to price it. I set up my future values for Fixed ...
0
votes
0answers
14 views

Why does the forward rate curve lies above the spot rate curve and the yield to maturity curve?

I saw a picture of 3 different yield curves, a spot rate curve, a forward curve, and a yield to maturity curve. The forward curve was at the top, the YTM curve at the bottom. I don't understand why.
1
vote
1answer
20 views

Compound interest calculator solving for time with deposits [on hold]

I am attempting to solve a compound interest calculation for time given Principal = 100 Time(years) = t Rate(per year) = 8% Deposit(per month) = 5 Total = 300 I ...
4
votes
3answers
70 views

Interest Rate Convexity - Fundamental Question

I have a very basic question around convexity adjustments in swap valuations. I am comfortable with the mathematical derivation of the convexity adjustment. My question relates to when and why a ...
3
votes
2answers
39 views

Integration to calculate expected value of swap rate

In Hagan's paper on valuing CMS swaps (Convexity Conundrums: Pricing CMS Swaps, Caps, and Floors), there is: So the swap rate must also be a Martingale, and $$E \big[ R_s(\tau) \big| ...
1
vote
0answers
43 views

Optimize a trading strategy created in excel with R

I have created quite a complex back test in excel spanning 15 years with 17 parameters. I would like to optimize the parameters which would give me maximum return given a maximum draw-down percentage. ...
1
vote
0answers
27 views

Bloomberg Historical Fundamental Data - Point in time

I'm trying to retrieve historical stocks fundamental data from Bloomberg to backtest some quant ideas. I'm having trouble to find the correct point in time the data was available. For instance, the ...
0
votes
0answers
10 views

If you could create a new type of option, what would it be? [closed]

I've been reading up on exotic options. The field is quite interesting and people have come up with all sorts of weird options, that go in the money if specific conditions are met. Here's a link to ...
0
votes
2answers
46 views

Can we derive 5 year zero coupon interest rate by using 1, 2 and 3 year zero coupon interest rate?

Given that the 1 year zero coupon bond interest rate is 5%, 2 year zero coupon bond interest rate is 6% and 3 year zero coupon bond interest rate is 7%. 4 year coupon bond price and interest rate are ...
0
votes
0answers
14 views

The equivalence of APV and WACC

How would you prove the equivalence of APV and WACC (for a firm with constant D/E ratio)?
0
votes
0answers
15 views

how to compute the call and put prices from the state-price vector? [on hold]

If I know the matrix a and vector p, I can derive the state price vector, but how can I derive the call price then?
0
votes
1answer
26 views

What are “df”, “t”, and “p” in these sharpe ratio related estimates?

I am looking at some sharpe ratio related estimates and have not seen Sharpe stats broken down this way before. I don't know what is meant by df, t, and p. Can someone explain that to me? Thank ...
0
votes
2answers
38 views

Portfolio Theory: Must VarCovar Matrix be based on return var/covar?

I am trying to estimate the minimum variance portfolio where the assets are currency derivatives. In the specific case it does not make sense to base correlations or variance on asset returns. I am ...
0
votes
2answers
74 views

The Difference between Notional and Par Value of a Bond

I have reached a confusing dilemma regarding the par and notional values of a bond. I have been told that the par value of a coupon bond is $100. However, the notional value of the bond is ...
0
votes
0answers
33 views

What are the top 30 high frequency trading firms in forex domain globally? [closed]

I am looking for top 30 high frequency trading firms,especially on forex globally, but its really difficult to get any info as nothing is out there. Can anyone enlighten me on this?
1
vote
1answer
54 views

Liquidity Traders

I am thoroughly reading my first academic literature and I have found myself overwhelmed by terms that have been generalised in my studies. The extract is from "The Beauty Contest and Short-Term ...
1
vote
2answers
39 views

Perpetual American options

Formulate and solve the free boundary problem for the perpetual American options with the following payoffs. a.) $(S - K)_{+} + a$ where $a > 0$ b.) $(K - S)_{+} + a$ where $a > 0$ ...
1
vote
1answer
38 views

given someone's past investing history, is there a way to calculate his risk aversion?

given someone's past investing history, is there a way to calculate his risk aversion? Say, we know this client's investment history for example his past return, is there a way to calculate his risk ...
6
votes
5answers
308 views

Thoughts on how quantitative hedge funds use machine learning to invest in the stock market (algorithms, examples of data, etc.)

I believe there are several post on this general topic but I thought I would start my own thread. I'm a former fundamental hedge fund investor (i.e. modeling a company's financials, forecasting the ...
0
votes
0answers
25 views

Evaluation of Bayesian GARCH

I am using the bayesGARCH package to estimate Bayesian GARCH models and I was wondering how to evaluate them in terms of precision of forecast or at least the quality of the model. I have encountered ...
0
votes
0answers
20 views

FX Counterparty Risk Modeling

We are building PFE model for FX derivatives including but not limited to outright and barrier options. For counterparty risk purpose, we are assessing whether black karasinski would be good for fx ...
0
votes
0answers
17 views

Comparison of quality across different fundamentals data sources?

There are a variety of different mechanisms and rules used by each fundamentals data provider to standardize and report company fundamentals. For example, the transformation of reported statements to ...
1
vote
1answer
59 views

Calculation of Bond Carry from Synthetic future prices

I have only government bond yields with different maturities. How can I obtain sythetic future prices on bonds? After obtained the future prices, I am supposed to compute the return and carry returns. ...
0
votes
0answers
26 views

is mean and variance sufficient to determine the following question?

consider this question: I want to buy AAPL, and I could buy it from 3 brokers. I have their historical quote. Is there any statistic other than mean and variance I could use to determine if one broker ...
0
votes
2answers
29 views

Regime switching model getting data

I am trying to find a dataset (oil prices, S&P index, DAX returns etc.) in order to visualize the high volatility and low volatility periods in a plot. So far, I have not found a dataset that has ...
2
votes
2answers
47 views

Automate selection of BIC-minimizing ARIMA(1,0,X) model

I want to estimate an ARIMA(1,0,X) model. The MA(X) in the model is selected to minimize BIC. I have the following code employing the function auto.arima from ...
0
votes
0answers
14 views

Hedging non-deliverable forward

For a non-deliverable forward, the payoff at maturity is $N(1-\frac{F}{S_T})$, where $N$ is the notional, $F$ is the forward rate predetermined at $t=0$, $S_T$ is the spot exchange rate at maturity ...
1
vote
1answer
52 views

Derivative: Delta of a Down and Out Call Option with Barrier=Debt(K)

I am trying to compute the derivative of this function with respect to V0: This is the price of a down and out call option, assuming the barrier equal to the level of debt K. In other terms, I need ...
0
votes
0answers
12 views

Value at Risk Backtest type 2 error

I am wondering why in the most popular tests(Kupiec's POF, Christoffersen, the Null hypothesis is "our model is accurate". If we set our null hypothesis that way, we only have a decent result if we ...

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