All Questions

2
votes
1answer
72 views
+50

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
49 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
147 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
25 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
51 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
76 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
42 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
76 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
31 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
70 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
133 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
51 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
77 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
65 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. ...
5
votes
1answer
89 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 $$\Omega=\{\omega=(y_1,\ldots,y_T)|y_i=\pm1\}$$...
8
votes
1answer
175 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
44 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
28 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
38 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
44 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
24 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
27 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
31 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
106 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/...
1
vote
0answers
18 views

Pricing a transfer option for oil

Need some input in how to attack this problem. Given are 8 timeseries: UK Oil price, Delivery Quarter 1 2020 UK Oil price, Delivery Quarter 2 2020 UK Oil price, Delivery Quarter 3 2020 UK Oil price, ...
0
votes
0answers
21 views

Perpetual bond valuation between coupon dates

According to this Derive Perpetual Bond Price , I learned how to derive the formula of perpetual bond. However, I still have some questions. Firstly, do I need to change the formula when valuing the ...
1
vote
0answers
38 views

ARCH; Expectation and Variance

I have got the following question that I am struggling to answer. The stock return $S_t$ follows the following DL model, with $Z_t$ being a dependent variable explaining the stock return: $S_t = \...
1
vote
1answer
57 views

Why financing costs are ignored in capital budgeting of projects?

Any finance textbook I have encountered including CFA materials states something like this: "Financing costs are ignored. This may seem unrealistic, but it is not. Most of the time, analysts want to ...
1
vote
3answers
91 views

Delta hedging pnl to recover option price

In Black Scholes framework, assuming zero interest rates and realized volatility to be same as implied volatility, gamma pnl is exactly same and opposite of theta pnl. So if I buy an option and delta ...
0
votes
0answers
27 views

Using Non-Risk Neutral (Risk Natural) Parameters to Price Options?

Please correct me if any of my following statements are false. My understanding as to why we use Risk Neutral Analysis is that it makes life easy, and ultimately, allows use to come to a closed form ...
1
vote
1answer
109 views

Reducing pricing errors (Alpha) in the CAPM with Bitcoin

I have been trying to examine, using the CAPM, if Bitcoin belongs in the market portfolio or not. With 10 industry portfolios from http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library....
1
vote
1answer
75 views

How does the Black Scholes Model Incorporate Log Prices Into Model?

I am still not understanding the link between log prices and how that is incorporated into the BS model. I understand why log(S) is assumed because it makes math easier and it prevents ending prices ...
1
vote
1answer
39 views

Calculating the max. risk free interest rate with two given options

I have an excercise where we have two European Call Options, which have the same underlying, same maturity $t = 3$, same interest. The only difference is their price and their strike. The price of the ...
0
votes
0answers
36 views

Value of a put > strike?

I dont understand why the value of a put will be greater than the strike. Is this human error? Weatherford had been delisted and the price of the underlying OTC is 0.05 at the moment. Its a 0.50 Put 6/...
0
votes
0answers
26 views

Expected Payoff of stock using risk neutral Valuation

I recently saw a calculation where the expected 10-state-payoff-diagram of a stock with mean 6% and variance 20% was calculated through the risk neutral measure. The method was as follow: ...
0
votes
0answers
34 views

Tangency portfolio with constraints

Hello to everyone I am trying to implement a version of MV optimization with constraints as UB and LB, it seems to work fine but now i was trying to figure out a simple way to derive a CML in the same ...
2
votes
0answers
44 views

sharp ratio/sortino ratio for options portfolio

I am thinking that the sharp ratio is not a valid performance metric for a long/short options book, because options are inherently nonlinear and the standard deviation simply cannot correctly capture ...
0
votes
0answers
26 views

GARCH, EGARCH, GJR with different distributions

I have estimated different models based on different distributions. Since they are not nested models of each other, I can't use LR tests. But how can I compare the models? Can I do something with the ...
0
votes
0answers
36 views

How to create optimal portfolio using copula functions? [closed]

How to create optimal portfolio using copula functions? If I know only returns of some stocks.
2
votes
0answers
27 views

Constraints by estimating GARCH, EGARCH, GJR-GARCH models

I know that by estimating an GARCH model, given by: $$\sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2,$$ $\omega, \alpha, \beta >0$ and $\alpha + \beta <1$. But what are ...
1
vote
1answer
36 views

rationale for maturity adjustment formula in basel IRB formula

For capital requirement, rwa is computed as a product of terms including a K (unexpected losses). (As shown is the summary from wikipedia : https://en.m.wikipedia.org/wiki/Advanced_IRB ) K is ...

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