Pricing bond options in emerging markets: A case study

Guillermo Magnou; Ernesto Mordecki; Andrés Sosa

doi:10.3934/jdg.2018003

Article Contents

2018, Volume 5, Issue 1: 21-30. Doi: 10.3934/jdg.2018003

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Pricing bond options in emerging markets: A case study

1.
Department of Legal Governance, Risk Management, and Compliance, AFISA SURA, L.A. De Herrera 1248 Torre 3 piso 16, Montevideo, Uruguay
2.
Centro de Matemática, Facultad de Ciencias, Universidad de la Repúlbica, Iguá 4225, CP 11400, Montevideo, Uruguay

Received: January 2017

Revised: September 2017

Published: January 2018

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Abstract

We propose two methodologies to price sovereign bond options in emerging markets. The motivation is to provide hedging protection against price fluctuations, departing from the not liquid data provided by the stock exchange. Taking this into account, we first compute prices provided by the Jamshidian formula, when modeling the interest rate through Vasicek model, with parameters estimated with the help of the Kalman filter. The second methodology is the pricing strategy provided by the Black-Derman-Toy tree model. A numerical comparison is carried out. The first equilibrium approach provides parsimonious modeling, is less sensitive to daily changes and more robust, while the second non-arbitrage approach provides more fluctuating but also what can be considered more accurate option prices.

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Mathematics Subject Classification: Primary: 91B25; Secondary: 62M05.

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Figure 1. Monthly returns of AFAPS. Year 2013 (in UYU).

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Figure 2. Example of a four period binomial tree.

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Table 1. Option prices for zero coupon USD (left) and UI bonds (right). VK and BDT stand for Vasicek and Black-Derman-Toy models respectively

USD 3 months option prices					UI 3 months option prices
Strike	CALL		PUT		Strike	CALL		PUT
Strike	VK	BDT	VK	BDT	Strike	VK	BDT	VK	BDT
$99.50$	$0.000$	$0.000$	$5.268$	$5.069$	$94.00$	$0.000$	$0.000$	$3.617$	$3.580$
$97.06$	$0.000$	$0.000$	$2.831$	$2.641$	$92.18$	$0.000$	$0.000$	$1.817$	$1.782$
$94.69$	$0.001$	$0.187$	$0.464$	$0.459$	$90.40$	$0.117$	$0.240$	$0.173$	$0.259$
$92.37$	$1.853$	$2.044$	$0.000$	$0.007$	$88.65$	$1.675$	$1.711$	$0.000$	$0.001$
$90.11$	$4.111$	$4.291$	$0.000$	$0.000$	$86.93$	$3.377$	$3.405$	$0.000$	$0.000$
USD 6 months option prices					UI 6 months option prices
Strike	CALL		PUT		Strike	CALL		PUT
Strike	VK	BDT	VK	BDT	Strike	VK	BDT	VK	BDT
$99.55$	$0.000$	$0.000$	$5.117$	$4.852$	$94.76$	$0.000$	$0.000$	$3.341$	$3.128$
$97.36$	$0.000$	$0.000$	$2.934$	$2.673$	$93.15$	$0.000$	$0.002$	$1.766$	$1.569$
$95.22$	$0.015$	$0.160$	$0.801$	$0.703$	$91.58$	$0.086$	$0.267$	$0.316$	$0.300$
$93.12$	$1.129$	$1.599$	$0.000$	$0.058$	$90.03$	$1.286$	$1.484$	$0.001$	$0.008$
$91.07$	$3.336$	$3.582$	$0.000$	$0.003$	$88.51$	$2.773$	$2.958$	$0.000$	$0.000$
USD 1 year option prices					UI 1 year option prices
Strike	CALL		PUT		Strike	CALL		PUT
Strike	VK	BDT	VK	BDT	Strike	VK	BDT	VK	BDT
$99.65$	$0.000$	$0.000$	$4.561$	$4.224$	$96.25$	$0.000$	$0.000$	$2.673$	$2.229$
$97.94$	$0.000$	$0.000$	$2.867$	$2.538$	$95.10$	$0.000$	$0.005$	$1.573$	$1.136$
$96.26$	$0.000$	$0.069$	$1.204$	$0.950$	$93.95$	$0.037$	$0.231$	$0.511$	$0.277$
$94.61$	$0.441$	$0.918$	$0.011$	$0.170$	$92.83$	$0.619$	$1.047$	$0.002$	$0.021$
$92.99$	$2.034$	$2.373$	$0.000$	$0.023$	$91.71$	$1.669$	$2.086$	$0.000$	$0.001$

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