Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2410.04748

Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysis

Jagdish Gnawali·W. Brent Lindquist·Svetlozar T. Rachev
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce a fairly general, recombining trinomial tree model in the natural world. Market-completeness is ensured by considering a market consisting of two risky assets, a riskless asset, and a European option. The two risky assets consist of a stock and a perpetual derivative of that stock. The option has the stock and its derivative as its underlying. Using a replicating portfolio, we develop prices for European options and generate the unique relationships between the risk-neutral and real-world parameters of the model. We discuss calibration of the model to empirical data in the cases in which the risky asset returns are treated as either arithmetic or logarithmic. From historical price and call option data for select large cap stocks, we develop implied parameter surfaces for the real-world parameters in the model.

Explore related subjects

q-fin.MFq-fin.PR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jagdish Gnawali, W. Brent Lindquist, Svetlozar T. Rachev. 2024-10-08. Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysis. https://arxiv.org/abs/2410.04748

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fixed-Income Pricing and the Replication of Liabilities

This paper develops a model-free framework for static fixed-income pricing and the replication of liability cash flows. The absence of static arbitrage across a universe of fixed-income instruments is equivalent to the existence of a strictly positive discount curve reproducing all observed prices. Linear programming duality then identifies the least-cost super-replication price with the largest value that any admissible discount curve assigns to the liability, so that the resulting bounds are attained and cannot be improved. Complementary slackness confines over-replication to dates that the optimal discount vector prices at zero, and a least-cost portfolio matches the liability exactly at no fewer dates than the rank of the cash-flow matrix. We also obtain generic uniqueness of that portfolio, an interpolation between quadratic hedging and super-replication, and a static treatment of swap--repo strategies. On US Treasury cross-sections the observed prices violate the law of one price, so that a discount curve must be estimated rather than bootstrapped; the least-cost portfolio then matches an annuity liability at almost every cash-flow date.

q-fin.MF↗
arXiv2026

Gatheral's Conjecture Revisited

We consider the Heston model with perfect negative spot--variance correlation and its one-dimensional local-volatility projection. Let $I_T^{\mathrm H}$ and $I_T^{\mathrm{LV}}$ denote their respective integrated variances over $[0,T]$. We establish the inequality \[ \mathbb{E}\bigl[(I_T^{\mathrm H}-K)^+\bigr] < \mathbb{E}\bigl[(I_T^{\mathrm{LV}}-K)^+\bigr] \] for every maturity $T>0$ and every strike $K>0$. Consequently, Heston integrated variance is strictly smaller in convex order than the integrated variance of the calibrated local-volatility model. This strict ordering gives a Heston-model counterexample to the convex-order inequality conjectured by J. Gatheral.

q-fin.MF↗
arXiv2026

Concave Shape of the Yield Curve and No Arbitrage

In fixed income sector, the yield curve is probably the most observed indicator by the market for trading and fifinancing purposes. A yield curve plots interest rates across different contract maturities from short end to as long as 30 years. For each currency, the corresponding curve shows the relation between the level of the interest rates (or cost of borrowing) and the time to maturity. For example, the U.S. dollar interest rates paid on U.S. Treasury securities for various maturities are plotted as the US treasury curve. For the same currency, if the swap market is used, we could also plot the swap rates across the tenors which would be called the swap curve.Even the yield curve can be at, upward or downward (inverted), however, yield curve is generally concave. There is a lack of explanation of the concavity of the yield curve shape from economics theory. We offer in this article an explanation of the concavity shape of the yield curve from trading perspectives.

q-fin.MF↗