All Questions
22,812
questions
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Influence of Yield on the Cheapest-To-Deliver bond to honour a short position on a treasury bond futures contract?
In Options, Futures and Other Derivatives 11e by John C. Hull section 6.2 in the subsection 'Cheapest-to-Deliver Bond', the author claims that:
A number of factors determine the cheapest-to-deliver ...
- 151
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19
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Resources to learn derivates [duplicate]
Actually I do follow investopedia but any other tried and tested resources would be helpful.
- 1
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0
answers
88
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Resources to learn stochastic calculus [duplicate]
I'm looking for a good resource to learn stochastic calculus but I'm not very good at calculus . So could anyone please tell whether the book Stochastic Calculus for Finance by Steven Shreve is a ...
0
votes
1
answer
102
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Delta of a currency forward contract that price follows Ornstein–Uhlenbeck process
Considering a currency forward contract that matures at time $T$, and its price $F_t$ follows the OU process such that
\begin{equation}
F_t = F_0 e^{-Kt} + a(1 - e^{-Kt}) + \sigma\int^t_0 e^{K(s-t)} ...
- 87
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38
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Stochastic exponential and Girsanov
Let's say I have an instrument $V$ with payoff at maturity: $P(S_T)$ (for example $1_{S > K}$) that I want to price under stochastic rates: $dr_t = \mu dt + \theta_t dW_t$, with $W_t$ a Brownian ...
- 51
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1
answer
41
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Bond Prices verse Yields [closed]
So maybe this isn't the right place for this question as it could be construed as an open-ended market speculation question the way I frame it, but I am trying to solidify my knowledge in regards to ...
- 101
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19
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Can an American option calendar spread have a negative price?
Consider an American put calendar spread on strike K with maturities T1 < T2. Is the longer-dated put always more expensive than the shorter-dated one?
How valid is the following no-arbitrage ...
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53
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Theoretical pricing models as time to expiry approaches
I was reading Option pricing and volatility by Sheldon Natenburg and in chapter 5 he says the following:
“Although traders typically express time to expiration in days, a trader may want to use a ...
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1
answer
85
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Black-Scholes formula for currency exchange rates
Exercise 17.6 of Options, Futures, And Other Derivatives by John Hull (Page 397):
Show that the formula in equation (17.12) for a put option to sell one unit of currency A
for currency B at strike ...
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45
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Canonical choice of inputs for Black76 model?
What is the canonical choice of inputs (e.g. interest rate, forward price, option price, time to expiration, etc) for the Black76 model? For concreteness let's say on the SPX index.
I am using the ...
user72785
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2
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58
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Pricing an option on the spread of two contracts, what correlation parameter?
I must price an option on the spread of two futures (A-B) the model I must use uses the IV on the options of each futures. Another parameter I need is the correlation of these, what would be a ...
- 23
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1
answer
60
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Interest rate to use in black scholes when rates of borrowing and lending are different
I was reading Option pricing and volatility by Sheldon Natenburg and he talks about interest rates and which interest rate to feed to the model. Here is the paragraph from the book(chapter 5):
"...
1
vote
2
answers
107
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How to interpret the physical meaning of cointegration vectors of log prices in real world
I'm trying to understand the physical meaning of cointegration vectors of log prices in the real world.
For example, if I have two assets $A$ and $B$, and Johansen test gives us a cointegration ...
- 21
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votes
1
answer
55
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risk-premium if we leave risk-neutral world
Risk neutral pricing in the Black-Scholes-Model makes life easy since it solves the challenge of the choice of two parameters simultanuously: the drift-parameter $\mu$ in the underlying geometric ...
- 1
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answers
39
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Where to find lookback options example？
I am a beginner in lookback options and I want to learn about real-world examples of this type of over-the-counter option. Where can I find practical examples? Thank you very much!
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1
answer
70
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Discounting on SOFR/SONIA/Euribor Options
I'm modelling the price of SOFR/SONIA/EURIBOR options on their corresponding futures. Is there a convention or details on whether discounting should take place or not? If there is no discounting why ...
- 25
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21
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Relationship between tenor and portfolio performance
I'm analysing the connection between the tenor of secured loan contracts and loan performance, represented by 30DPD@3MOB and 90DPD@12MOB (dummy variables).
I'm using logistic regression, which ...
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0
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53
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When Is Periodic Profit-Taking Better Than Holding Until Maturity?
I am conducting a comparative analysis of two investment strategies using Monte Carlo simulations: periodic profit-taking and holding the investment until maturity. Specifically, I am simulating price ...
- 482
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1
answer
44
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Incremental Variance Estimations on SPX
I am developing a program aimed at estimating the daily implied volatility of SPX using an incremental variance approach. My current methodology involves employing a root-finding algorithm coupled ...
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-2
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1
answer
107
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Properties of Stochastic Processes : Stopping times [closed]
Consider the probability space $(\Omega, \mathcal{F}, \mathbb{P})$ and the filteration $(\mathcal{F}_t)_{t\geq 0}$ i-e $$\mathcal{F}_t \subset \mathcal{F}_s \subset \mathcal{F}, \forall{t} < s $$
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67
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How to convert 3M IRS rate to 6M IRS rate without using basis swap?
I have a spot curve where the front-end points (1Y, 2Y) have a fixed/float frequency of 3M3M, while the rest of the points are 6M6M. I want to build a full 6M6M curve.
My question is: How can I derive ...
- 1
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votes
1
answer
49
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Model for this price dynamic
I would like to know if someone has idea on how to simulate the corresponding price dynamic :
The price moves x% hourly on either direction.
The maximum the price can move up in a day is y%, and the ...
- 98
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answers
40
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Intuition behind conversion factors increasing/decreasing for longer dated expiries?
I'm trying to intuitively reason why the below claim from The Treasury Bond Basis is true.
Conversion factors are unique to each bond and to each delivery month.
Note in Exhibit 1.3 that conversion ...
- 209
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votes
1
answer
99
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Signal update frequency and predicting directional return one step ahead
I am trying to get some insights on this specific sort of problem from experienced people, as I do not have much experience in this field.
I have a family of features that for simplicity I will just ...
- 105
2
votes
1
answer
379
views
Ratio of real world to risk-neutral density
Suppose I have a risk-neutral pdf and a real-world pdf of an asset. Both functions are related by a scaling factor or the sdf which would transform the risk-neutral into the real-world density, is ...
- 31
1
vote
1
answer
122
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Kelly Criterion for finite rounds
I understand that the Kelly criterion maximizes long-term utility under a log-wealth function, but from what I've gathered, this is only true if we have an arbitrarily high number of betting rounds. ...
0
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0
answers
32
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Quantlib Heston MC Discrepancy between methods
I am a newbie at Quantlib (not finance) and am trying to price with the Heston model. I have implemented two different ways to verify the correctness of the Heston path generation to use in a custom ...
- 233
1
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0
answers
42
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Pricing option with k-branch binomial tree, risk neutral pricing
Suppose I have a binomial tree with 4 branches, \$14,\$19, \$24, \$28. I have a call option with strike K=20. How would I compute the price of the call option while respecting risk neutral ...
- 11
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2
answers
123
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Options on Futures: Estimating implied volatility
In a commodities futures market, where there are options for the terminal expiry, whose implied volatility can be determined, I am interested in understanding what the implied volatility for an early-...
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44
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What $T$ to use a few hours till expiry when calculating implied volatility?
I am trying to calculate the implied volatility given an option price that is a few hours till expiry. The issue I am having is that I am not sure if it's better to use $T=\frac{1}{365}$ (case 1) or $...
- 99
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vote
1
answer
80
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Heston Model numerical instabilities
I hope that all is well,
I am working on creating a neural network to compute the implied volatilities of options using the Heston Model. However, I am coming across some issues with the numerical ...
- 57
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votes
1
answer
47
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The Intuition Behind The Max and Min of a Dual Digital
How do we intuitively figure out what the max and min price of a dual is? We know that the factors to price a dual is the price of digital option 1 and price of digital option 2 as well as correlation....
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votes
1
answer
81
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Nelson-Siegel-Svensson: question regarding data format for fitting the model
If I want to fit the Nelson-Siegel-Svensson (NSS) model to a set of spot, forward, or discount rates, my intuition says that the data should of course be in percentage form.
For example, I should use $...
- 117
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0
answers
22
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Charting software for SOFR future calendar spreads
trying to chart SOFR calendar spreads in TOS, but the wicks are way too long to be accurate. It's showing 50bps swings daily but that isn't right. Are there any alternatives?
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answers
37
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Why trade credit is considered as an investment
One of the Foreign Direct Investment (FDI) components is debt. I understand that a loan given from a foreign investor to an affiliate company in another country is a form of investment as there will ...
- 101
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0
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57
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How to estimate the diffusion matrix $\Sigma_0$ in Li and Papanicolaou, Applied Mathematics & Optimization (2022)?
In Li and Papanicolaou, Applied Mathematics & Optimization 86, 12 (2022), a key step is the determination of the diffusion matrix $\Sigma_0 = \Psi_0\Psi_0^T$ with $\Psi_0\in \mathbb{R}^{m\times (d+...
- 11
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1
answer
48
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Can derivatives of non-lognormal securities be priced using risk-neutral evaluations assuming risk-free drift?
The Black-Scholes model essentially says that, if we assume some things (lognormal, constant variance, etc.) then the following the fair price of a
$$C = N(d_1) S_t - N(d_2) K e^{-rt}$$
However, ...
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0
answers
39
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How Do I incorporate the basis spread between 2 currencies in a forward deal?
Lets assume I'm doing a yen/usd fx forward, the yen is my domestic currency. The basis spread between these currencies tells me the demand for 1 currency relative to the other.
The formula for an fx ...
- 1
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0
answers
68
views
Calculating Daily Returns for a Zero Net Investment Portfolio
I'm trying to create a zero net investment portfolio in an equally weighted manner using daily holding period returns for stocks. Here is my setup:
Day 1:
Long: Stocks A, B, C
Short: Stock D
Day 2:
...
- 286
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votes
1
answer
30
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Charging for cashflow mismatch in Liability Driven investment
I am doing a course on LDI and the following question came up:
We are given a liability schedule. The liability is backed by a bond paying fixed coupons. The bond and the liability have the same PV ...
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0
answers
41
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Options on SOFR Futures + SONIA futures modelling
I am modelling options on SOFR and SONIA futures using the Bachelier model (under a first approximation). The discounted price for a call option is
$$
C(K) = e^{-rT}[(F_0 - K)N(d) + \sigma\sqrt{T}n(d)]...
- 25
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1
answer
74
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Understanding Key Rate Durations in a Swap
As I understand, the Cashflows of a Payer-Swap are nothing else than being long a floating-rate bond and short a fixed-rate bond. So, to calculate the Key Rate Durations of the Swap I should be able ...
1
vote
1
answer
379
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Log return on short selling when the loss exceeds 100%
I'm working on a theoretical portfolio that includes both long and short positions. I already have the daily holding period returns, and I want to calculate both arithmetic and logarithmic returns for ...
- 286
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vote
1
answer
157
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Bond Futures why CTD driven by yields?
Can you please explain with a numerical example why long duration bonds (low coupon, long maturity) are CTD when yields are significantly greater than the contract standard coupon and when yields fall ...
- 45
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0
answers
56
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Calculating greeks for a combination of SPX and VIX options
I am trying to properly calculate the delta, vega and theta for an options strategy that involves buying a 90 day ATM SPX put and selling a 90 day ATM VIX call.
Here is what I have done so far:
SPX = ...
- 191
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0
answers
53
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correlation between bid/ask prices and bid/ask sizes to realized volatility
I am trying to understand the effect of correlation between bid price and ask size with realized volatility (called targe_vol). Similarly, correlation between ask price and bid size with realized ...
- 101
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1
answer
66
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ABM Crossing Times
Suppose I have a process that follows an arithmetic brownian motion
$dX_t = \sigma dW_t$
How do I calculate, within a certain interval $\Delta t$
, the expected number of times that the process will &...
1
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0
answers
52
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Change in Option Price given Change in Implied Volatliity, Moneyness, and Maturity
I have an implied volatility surface parametrized into moneyless-maturity coordinates. At each period of time, I only have access to an option's moneyness (K/S), maturity, and change in implied ...
- 11
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0
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73
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Modeling Yield Scenarios and Curve Shocks for Bonds
I would like to do the following:
Given a basket of bonds I want to generate different yield scenarios at a future time $T$ for the different bonds in my basket. I also want to see how I can shock the ...
- 51
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1
answer
109
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How to properly calcualte Realized Variance for WTI?
I have several realized variances for WTI, RV, scaledRV, RSVN(negative) and RSVP(positive), which were given to me by a professor whom I cant contact anymore. When I try to calculate my own RV (in ...
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