Python for Finance

by | Feb 22, 2023 | finance

 

We know from finance that a coupon bond can be priced as follows:

π‘ƒπ‘Ÿπ‘–π‘π‘’=𝑃(π‘π‘œπ‘’π‘π‘œπ‘›π‘ )+𝑃𝑉(π‘“π‘Žπ‘π‘’ π‘£π‘Žπ‘™π‘’π‘’) , where the discount rate is known as the yield to maturity (YTM).

It is a known problem in finance that we cannot use a closed form solution to solve for the YTM but that we need to rely on an optimizer. Similarly to the code for how to optimize a portfolio you can use scipy’s minimize() to compute the YTM of a bond with certain parameters.

Task 1 [5 marks]
Write a function that takes the following inputs and computes and returns the YTM for a coupon bond with annual coupons:
Price
Coupon amount
Face value
Number of years until maturity

When you optimize for the YTM, you need to set the objective function to minimize. Use the following error definition:

γ€–βˆš((calculated) price from optimisation-reference price)γ€—^2
The reference price is what you are trying to get the optimizer to arrive at and the calculated price is the price the optimizer is computing with different values of YTM. Explain what is the advantage of this error function? Use your function on these parameters: Price = 1054; Coupon = 100; Face value = 1000; N = 10. (You should only provide the code).

Task 2 [5 marks]
Perform a sensitivity analysis on:
a. Price: varying from 900 to 1100 in steps of 1.
b. Number of years until maturity (N): varying from 1 to 50.

Use the parameters from part 1. Show your results graphically (Price or N on x-axis and YTM on y-axis) and explain why you see what you see from an economic perspective. Provide at least 1 paragraph of text per graph! (Max 100 words per paragraph)

 

 

 

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell.Β 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.


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God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that β€œarrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.

 

References

Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them.Β Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro.Β Cultural and Religious Studies,Β 4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27.Β Italica, 285-297.

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