All Questions

0
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0answers
4 views

How to add Risks-Not-In-VaR (RNIV) to VaR under Basel III

I am trying to generate/prove the magnitude of the over-conservativeness of the regulatory VaR (internal models) under Basel III against what a more accurate VaR would be. However, I can't seem to ...
0
votes
2answers
28 views

Why can we assume that asset return rates are normally (or lognormally) distributed?

In many theories of financial mathematics it is assumed that asset return rates are normally distributed (e.g. VaR models) or lognormally distributed (e.g. Black-Scholes model). In practice, asset ...
1
vote
0answers
19 views

Constructing Portfolio Beta

Suppose I have a portfolio with securities with different history. Say some securities have 15-20 years of history and some are like Uber or Lyft, which has limited history. There are assets with 1/2/...
1
vote
1answer
28 views

Covered Interest Rate Parity with FX Spot-Adjustment

The Covered Interest Rate Parity for FX is often quoted simplistically as $$ X_T \quad=\quad X_S \cdot \frac{D^{base}_T}{D^{quote}_T} $$ where $X_t$ is the (projected) FX rate at time $t$ (denoted as $...
0
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0answers
18 views

Distribution of the Information Ratio // Mean and Variance Product

We are investigating the distribtuion of the information ratio. However, instead of using the original information ratio defined as \begin{equation} IR=\frac{E(r_1)-E(r_2)}{\sqrt{Var(r_1-r_2)}}, \end{...
0
votes
2answers
31 views

Is it possible to adapt Fama French Model with a 6 factor Model?

I am currently working on my thesis and I was wondering if it was possible to add a new factor to the five model one. This new factor would include the ESG's characteristic of the stock. I would like ...
0
votes
1answer
44 views

When a bank enters a swap with a counterparty, when does it decide to use a OIS curve as its CSA Term, versus a counterparty specific “CSA Curve”?

What determines whether a swap should be discounted against a standard OIS curve VS a 'custom' CSA curve specific to the swap's counterparty? (such custom curves are marked as spreads to some base ...
1
vote
1answer
39 views

Forecasting a seasonal series with R

I am working with the program "R". I used the command "seas (X-13)" to deseasonalize my quarterly series, then I did the forecast with it. Therefore my forecast is in deseasonalized terms. Now, I was ...
0
votes
0answers
12 views

Longstaff Schwartz with future conditional coupons

I've implemented the L-S algorithm for a simple put option. I want to value a more complex derivative which has future conditional coupons which only occur if the option is in the money. How would I ...
1
vote
0answers
23 views

Understanding the ZABR model (an extension of SABR)

http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf In this acticle the SABR model is first presented in another form ( see equation 7 in the article ) and then extended to the so called ZABR ...
0
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0answers
39 views

A stringent test of stock return predictability? The role of one-sided hypothesis tests

A stringent test of stock return predictability? The role of one-sided hypothesis tests... In a well-published paper, Trading Volume and Cross-Autocorrelations in Stock Returns TARUN CHORDIA ...
1
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0answers
46 views

Is it necessary for $P(K, t) - P(K + s, t) \geq se^{-rt}$ to hold?

Let $P(K, t)$ be a put option with strike price $K$ and expiration time $t$. Let $s > 0$. Is it necessarily true that the inequality $$P(K, t) - P(K + s, t) \geq se^{-rt}$$ holds? I know that ...
0
votes
0answers
52 views

Portfolio - Default Probability

Suppose we want to identify the frequency of default on a portfolio with a 1000 loans. In the independence case, each firm’s default process follows a Bernoulli distribution with parameter $p = 0.01$. ...
1
vote
0answers
26 views

Pricing call option on bond under CIR model by simulating noncentral chi square distribution

In the original paper of CIR model, there is a pricing formula about call option on bond $$ \begin{array}{l}{C(r, t, T ; s, K)} \\ {=P(r, t, s) \chi^{2}\left(2 r^{*}[\phi+\psi+B(T, s)] ; \frac{4 \...
0
votes
2answers
75 views

Transaction costs in option market

The transaction costs in option market could be quite large. The bid ask spread of a SP500 firm could be around 15% of the mid-quote when I check the data. Since I do not have data on transaction ...
1
vote
0answers
43 views

How do you hedge with delta futures if payment is unsure?

A Czech company has a payable of 1,5 mil EUR that has got a settlement at the end of the current month and at the same time it is expecting a payment of 1,5 mil EUR at the half of the current month ...
1
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0answers
45 views

Mean-variance portfolio optimization: methods for superior estimates of returns

Leaving aside the aspects related to the estimation of the variance component (all the latest techniques to compute a stable covariance matrix of a given set of assets such as simple shrinkage, Ledoit-...
1
vote
1answer
45 views

Calculating PD of commercial bank loan

I have two main options to calculate PD of a loan in a commercial bank; with and without machine learning. On one hand, there are traditional methods such as Merton or KVM. On the other hand, I could ...
1
vote
0answers
45 views

Why don't we build the discounting curve and projection curve from bonds

We know that we always build the discounting curve and projection curve from money market instruments, index Futures, interest rate swap and OIS Libor swap (depends on the period). But why don't we ...
1
vote
1answer
58 views

Leverage constraints

I am trying to complete my project on Mean-Variance Leverage Optimization, and I have found lots of helpful advice on this forum. I wanted to ask you if you have some idea on how to implement a ...
2
votes
1answer
133 views

Pricing under risk-neutral probabilities for weird derivatives?

I would really appreciate some help to value a weird derivative that I've found in an assignment: $$ X=(S_{T_1}-k)^{+} = \max(S_{T_{1}}-k;0) $$ which expires at time $T_{2}$ and uses the price at ...
1
vote
0answers
24 views

How to apply multiplicative price seasonality to bond prices in quantlib?

Can someone please give a brief or any link which explains how to apply multiplicative price seasonality to inflation linked bonds in Quantlib using python modules. Have gone through most of the ...
1
vote
0answers
48 views

Does Vasicek interest rate model had any derivation that follows from a list of assumptions?

I can't find that anywhere online and It doesn't seems to me that this model originated come from intuition or some human motivation but rather it is coming from computerized curve fitting as all the ...
1
vote
1answer
66 views

In-sample volatility measurement

I would like to know what is the most reasonable way to measure volatility in a sample of past observations. Aside from standard deviation, are more complex models like GARCH used for (historical) ...
3
votes
0answers
41 views

Why not discount the dividend in the european put lower bound condition?

According to the european put lower bound condition: $ p \geq max(D + K \cdot e^{-r(t_2-t_0)} - S_0, 0)$ where $t_0$ is now and $t_2$ is maturity. Say $t_1$ is the dividend release time where $t_0&...
2
votes
1answer
70 views

Hedging with different volatility (Ahmad and Wilmott paper)

In their paper they show that: - if you hedge with the realised volatility, the present value of the total p&l is the difference between the option value based on the realised volatility and the ...
1
vote
1answer
30 views

Cross currency swap basis with USD added on the covered interest rate parity (CIP)

We know the adjusted covered interest rate parity (CIP): $$Forward = \dfrac{1+r\cdot\tau+b}{1+r^*\cdot\tau+b^*}Spot$$ Here $r/r^*$ is the risk-free foreign/domestic rate and $b/b^*$ is the cross ...
2
votes
0answers
67 views

Quantitative Finance books for Practitioners [duplicate]

Currently searching for some books on real options and option pricing. However, the vast majority of the books are quite theoretical, and if someone has been taught these subject in class, half of it ...
3
votes
1answer
125 views

Finding optimal trading of option on a foward

Assume you have a option on a forward $F$ with a payoff: $\max(F_T - K, 0)$. Assume also, that you have a bullish view on the forward in such a way that $E_{0}[F_T] > F_0 = E_{0}^{*}[F_T]$ (where ...
4
votes
1answer
43 views

Stress Testing approaches at Pension Funds/Asset Management companies

I am looking for resources on Stress Testing for non-banking institution, specifically for long term oriented Asset Management companies, Hedge Funds, Pension Funds, and other Investment companies. ...
1
vote
1answer
76 views

Discontinuous derivative payoff approximation

Consider a derivative of digital type which pays this kind of payoff at time $T$: \begin{align*} g(S_T,k) &= \begin{cases} P_0,~S_T>k \\ S_T, ~S_T\leq k \end{cases} \end{...
1
vote
1answer
20 views

Term structure model for exchange-traded STIR futures and their options

As I understand, models such as the SABR extension of the Libor Market Model are the "standard" for interest rate derivative valuation in OTC markets, where options tend to be European and it is ...
1
vote
1answer
61 views

Cross currency basis swap for bonds

Running a cross currency swap on a GBP issued 2.75% 7yr bond (i.e a bullet), with funding in USD so need to determine the equivalent in USD. The GBP bond trades at circa 180bps over the Gilt. ...
4
votes
1answer
78 views

Expected value of exponential of hitting time of GBM

We have a stopping time $$ \tau=\inf\{t\geq 0: S_0e^{\sigma B_t+(r-\sigma^2/2)t}=S^* \} $$ where $S_0,\sigma,r,S^*$ are constants and $S^*<S_0$, and $B_t$ is a brownian motion. I wish to compute ...
1
vote
1answer
44 views

CRR model arbitrage free

I'm currently studying this proof In this proof the author defines a probability measure $$P^*[\{\omega\}]=(p^*)^{k(\omega)}(1-p^*)^{T-k(\omega)}$$ on $$\Omega=\{\omega=(y_1,\ldots,y_T)|y_i=\pm1\}$$...
6
votes
1answer
135 views

Why not just be long VIX and wait for the next volatile period?

Over the past 3 months, VIX has been relatively low. Therefore, there seems to be a "free-lunch" here by just being long VIX, and wait for the next market turmoil (which is happening at the moment ...
1
vote
0answers
43 views

Time weighted Vega for a VIX future contract

How to calculate the time weighted Vega applicable for a 3 month future contract (Expiring in 82 days)? Vega with S&P500 as base
1
vote
0answers
27 views

Log Contract payoff function

I can’t get where Dr. Rouah gets payoff function of log contract. Could you please take a look at that? https://frouah.com/finance%20notes/Variance%20Swap.pdf It’s on page 2, section 3. I couldn’t ...
0
votes
0answers
30 views

Radon-Nikodym for different distributions [closed]

I have probably a very stupid question but is the radon nikodym of a Bachelier Model is equivalent to a Black Scholes model? Can someone explain me that with not to difficult mathematics? Thank you ...
0
votes
0answers
37 views

What is the model behind Heston-Nandi functions in the fOptions R package?

I am dealing with Heston model in R and for this purpose I am using the package fOptions from RMetrics. The calibration formula requires the specification of some parameters (omega, lamda, alpha, ...
1
vote
1answer
50 views

Python Numpy FFT array size limit?

I am trying to find the price of an Option based on the fft technique within the binomial model and it works fine until N>40000 where I start getting negative values and weird convergene and I am not ...
0
votes
0answers
36 views

Calculation of Conditional Expected Value and Pay-Off Diagram

I have a stock with mu 6% and sigma 20% following a random walk and I would like to to calculate the Conditional expected Value of the stock in 10 states with equal probability (10%). Meaning, I would ...
1
vote
0answers
18 views

How to calculate a prepayment penalty on a mortgage

I have issued 2 mortgages...one with an option to prepay the loan, the other without that option. I want an objective way of calculating the extra interest rate (compared to the second) and ...
1
vote
1answer
49 views

Finding the extrinsic value of an option with conditions

Background: Consider a spread option with the payoff $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant. Let's also assume, that the correlation ...
0
votes
0answers
27 views

Mean-reverting Ornstein-Uhlenbeck Process [closed]

Can any of you help me derive the Expectation and variance of the Mean-reverting Ornstein-Uhlenbeck Process as the limit tends to infinity?
0
votes
1answer
43 views

Multi-legged Swap pricing

can anyone guide me how to price a multi-legged swap and whether I need Monte Carlo / LMM based approach or if there is a closed form solution. Receive leg "Libor 3m +1%" Payment leg If Libor is ...
0
votes
0answers
22 views

Are pure PIK bonds' payoffs known from the start?

I am developer working in the financial field and I would like to understand what I'm doing. My latest work subject involves Payment In Kind bonds with coupons fully reinvested (e.g, no coupons ...
1
vote
0answers
26 views

Numerical Solution to 3 Dimensional Backward BS PDE

I have a three dimensional backward BS PDE. $$ \frac{\partial V}{\partial t} + a(t) S \frac{\partial V}{\partial S} + \frac{1}{2} \sigma(t, S)^2 \frac{\partial^2 V}{\partial S^2} + b(t, M) \frac{\...
0
votes
1answer
30 views

Rationale for likelihood function parameter choice in Black-Litterman model?

So we are interested in a PDF for equilibrium returns given the views. Why do we choose our view means as the mean parameter and observed market covariance as the covariance parameter? Seems a bit ...
0
votes
1answer
103 views

A volatility model developed by JP Morgan

I am quite confused with this predicting volatility equation: σ2t = βσ2t-1 + (1-β)ε2t Here is a section from Capital Market Expectations: CFA Level 3 Volume 3 Curriculum (page 27) https://ibb.co/...

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