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Road
Road
Written by	Jim Cartwright
Date premiered	1986
Place premiered	Royal Court Theatre Upstairs; London, England
Original language	English
Subject	Thatcher's Britain, Unemployment
Setting	1980s, A town in Northern England

Plasticine
Plasticine
Written by	Vassily Sigarev translated to English by Sasha Dugdale
Date premiered	1998
Place premiered	Royal Court Theatre; London, England
Original language	English (translated from Russian)
Subject	Contemporary Russia
Genre	satire
Setting	1990s, Russia somewhere

Plasticine is a satirical play written by Vassily Sigarev first staged in London in 1998. Its subject is the

Valuation

The market practice for valuing European Swaptions is to use the Black model, with the annuity factor of the swap as the "discount factor" and the par swap rate as the "forward".^[1] In this way the only parameter driving the value of the Swaption is the volatility.

The use of the Black model can be theoretically justified (for physical Swaptions) as follows.^[2] We start with the general form for the value of a payer swap, with notional equal to 1 (see Interest rate swap § Valuation and Pricing),

P_{T}=(S_{T}-K)A_{T},

where $A_{T}$ is the value of the annuity factor of the fixed leg of the swap, $S_{T}$ is the par swap rate and $K$ is the agreed fixed rate of the swap. Using the fundamental theorem of mathematical finance, we consider the measure with the annuity $A_{t}$ as numeraire (known as the annuity measure), and get the general result:

P_{t}=A_{t}\mathbb {E} ^{\mathbb {Q} _{A}}[P_{T}/A_{T}].

We therefore have the swaption value at times $t\leq T$ as

P_{t}=A_{t}\mathbb {E} ^{\mathbb {Q} _{A}}[(S_{T}-K)_{+}].

Finally, because the par swap rate is the ratio of the value of the floating leg to the annuity factor, it must be a martingale (probability theory) in the annuity measure, so that the par rate of the forward swap $S_{t}=\mathbb {E} ^{\mathbb {Q} _{A}}[S_{T}]$ . So if we assume this swap rate follows a Geometric Brownian Motion, the value will be given by the Black formula. Note that the moneyness of a swaption will be defined by whether the fixed rate of the underlying swap is higher, lower or at the same level as the forward swap rate $S_{t}$ .

The volatility parameter can vary for different strikes, expiries, and swap lengths (i.e., an implied volatility surface), which takes away the reliance on the assumption of log-normality. Standard practice in the market is to use an extended version of the SABR volatility model to describe the volatility smile for a given expiry and swap length. ^[3]

Valuation (old)

The valuation of swaptions is complicated in that the at-the-money level is the forward swap rate, being the forward rate that would apply between the maturity of the option—time m—and the tenor of the underlying swap such that the swap, at time m, would have an "NPV" of zero; see swap valuation. Moneyness, therefore, is determined based on whether the strike rate is higher, lower, or at the same level as the forward swap rate.

Addressing this, quantitative analysts value swaptions by constructing complex lattice-based term structure and short rate models that describe the movement of interest rates over time.^[4]^[5] However, a standard practice, particularly amongst traders, to whom speed of calculation is more important, is to value European swaptions using the Black model. For American- and Bermudan- styled options, where exercise is permitted prior to maturity, only the lattice based approach is applicable.

To use the lattice based approach, the analyst constructs a "tree" of short rates—a zeroeth step—consistent with today's yield curve and short rate (caplet) volatility, and where the final time step of the tree corresponds to the date of the underlying swap's maturity. Models commonly used here are Ho–Lee, Black-Derman-Toy and Hull-White. Using this tree, (1) the swap is valued at each node by "stepping backwards" through the tree, where at each node, its value is the discounted expected value of the up- and down-nodes in the later time step, added to which is the discounted value of payments made during the time step in question, and noting that floating payments are based on the short rate at each tree-node. Then (2), the option is valued similar to the approach for equity options: at nodes in the time-step corresponding to option maturity, value is based on moneyness; at earlier nodes, it is the discounted expected value of the option at the up- and down-nodes in the later time step, and, depending on option style, of the swap value at the node. For both steps, the discounting is at the short rate at the tree-node in question. (Note that the Hull-White Model returns a Trinomial Tree: the same logic is applied, although there are then three nodes in question at each point.) See Lattice model (finance) § Interest rate derivatives.
In valuing European swaptions using the Black model, the underlier is treated as a forward contract on a swap. Here, as mentioned, the forward price is the forward swap rate. The volatility is typically "read-off" a two dimensional grid of at-the-money volatilities as observed from prices in the Interbank swaption market. On this grid, one axis is the time to expiration and the other is the length of the underlying swap. Adjustments may then be made for moneyness; see Implied volatility surface under Volatility smile.

Summary

The play starts with Rochester talking to the audience, and asking them not to like him. The first scene is in a coffee shop where Etheredge and something are reading through a pirate copy of the latest play by Dryden, in order to create a parody. They vocalise their wish that Rochester was with them as he is the "best to bring wit", explaining at the same time how he has been banished from London for reciting obsecenities to King Charles in public. At this moment Rochester appears. They decide to head to the playhouse.

Scene 2 - a play starts (which?) with Elizabeth Barry playing a minor role. She aims to act in a "true" fashion, in contrast to the fashion of the time, and is roundly booed by the audience, except that we see that Rochester is spellbound. After the play Rochester comes to see Barry and offers to train her in acting..........

?? Wife arrives...

Meet the king, with young lad... King asks Rochester to write him a play "to be pride of nation(?)"

Pall Mall - Wife there, gives speech. Barry turns up quoting Ophelia (?) Mallett understands that Rochester has fallen in love with Barry, and decides to go back to the Country Home.

Craziness of Merry Gang - smashing up the sundial. Exposing violence of Rochester.

Windsor - rehearsing Rochester's play, Sodom, the King arrives unexpectedly and demands to see the portrayal of the king. (explain something about the play....) It becomes clear that he has seen a copy of the script. Once the rest of the party leaves, Charles vents his anger at Rochester and, once again, banishes him from London.

Epsom- Merry Gang plus Barry watching the horses - Rochester apart, making couplets. SOmething goes wrong for Rochester...(?)

East End

PLayhouse - putting on Etheredge's play, The Man of Mode, based on Rochester. Conversation in the wing between Barry and Rochester. Rochester states his love and asks Barry to marry. Barry refuses, preferring to build a career as a famous and creative actress rather than give this up "like Nell Gwynn", but she admits she is pregnant with Rochester's child.

Home - Rochester wakes Mallett on arriving home, and asks for more drink. Conversation about his life....

Controversies

The theatre has been subject to various controversies over the years, for example:

Perdition by Jim Allen (1987). Its premiere at the Theatre Upstairs in London was abandoned, after protests, because of the controversial and tendentious claims it contains.
Seven Jewish Children by Caryl Churchill (2009). Many Jewish leaders and journalists criticised the play as antisemitic.

^ Hull, John (2013). Fundamentals of Futures and Options Markets (eighth ed.). Pearson. p. 662. ISBN 978-0132993340.
^ Joshi, Mark (2008). The Concepts and Practice of Mathematical Finance. Cambridge University Press. p. 292. ISBN 978-0521514088.
^ something
^ Frank J. Fabozzi, CFA (15 January 1998). Valuation of Fixed Income Securities and Derivatives. John Wiley & Sons. pp. ^{&#91, page needed&#93,}. ISBN 978-1-883249-25-0.
^ "Option valuation" (PDF). Fall 2000. Retrieved May 2014. {{cite web}}: Check date values in: |accessdate= (help)^{[full citation needed]}

[1] Hull, John (2013). Fundamentals of Futures and Options Markets (eighth ed.). Pearson. p. 662. ISBN 978-0132993340.

[2] Joshi, Mark (2008). The Concepts and Practice of Mathematical Finance. Cambridge University Press. p. 292. ISBN 978-0521514088.

[3] something

[4] Frank J. Fabozzi, CFA (15 January 1998). Valuation of Fixed Income Securities and Derivatives. John Wiley & Sons. pp. ^{&#91, page needed&#93,}. ISBN 978-1-883249-25-0.

[5] "Option valuation" (PDF). Fall 2000. Retrieved May 2014. {{cite web}}: Check date values in: |accessdate= (help)^{[full citation needed]}

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